International Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110120170126A study on the differential and sub-differential of fuzzy mapping and its application problem117http://dx.doi.org/10.22436/jnsa.010.01.01 ENYu-EBaoCollege of Mathematics, Inner Mongolia University for Nationalities, Inner Mongolia, Tongliao City, 028043, China.Jin-JunLiCollege of Mathematics, Inner Mongolia University for Nationalities, Inner Mongolia, Tongliao City, 028043, China.In this paper, firstly, we gain some basic properties and characterization theorems of the differential and local sub-differential
of the fuzzy mapping, obtain an important result that the local sub-differential of fuzzy mapping is an empty set or a convex
set. Secondly, we generalize the concept of local differentiability of fuzzy mapping, and obtain some basic properties about
the concept. At last, we study the relationships between sub-differential of fuzzy mapping and differential of convex fuzzy
mappings. Moreover, a sufficient condition that a class of fuzzy mapping have convex extension is gained.
http://isr-publications.com/jnsa/3092/download-a-study-on-the-differential-and-sub-differential-of-fuzzy-mapping-and-its-application-problemInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110120170126Fixed point theorems of nondecreasing order-Ćirić-Lipschitz mappings in normed vector spaces without normalities of cones1826http://dx.doi.org/10.22436/jnsa.010.01.02ENZhilongLiSchool of Statistics, Jiangxi University of Finance and Economics, Nanchang, 330013, China.ShujunJiangDepartment of Mathematics, Jiangxi University of Finance and Economics, Nanchang, 330013, China.We introduce the concept of order-Ćirić-Lipschitz mappings, and prove some fixed point theorems for such kind of mappings
in normed vector spaces without assuming the normalities of cones by using upper and lower solutions method, which
improve many existing results of order-Lipschitz mappings in Banach spaces or Banach algebras. It is worth mentioning that
even in the setting of normal cones, the main results in this paper are still new since the sum of spectral radius or the sum of
restricted constants may be greater than or equal to 1.http://isr-publications.com/jnsa/3093/download-fixed-point-theorems-of-nondecreasing-order-ciric-lipschitz-mappings-in-normed-vector-spaces-without-normalities-of-conesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110120170126On order-Lipschitz mappings in Banach spaces without normalities of involving cones2733http://dx.doi.org/10.22436/jnsa.010.01.03ENZhilongLiSchool of Statistics, Jiangxi University of Finance and Economics, Nanchang, 330013, China.ShujunJiangDepartment of Mathematics, Jiangxi University of Finance and Economics, Nanchang, 330013, China.RadeLazovicFaculty of Organizational Sciences, University of Belgrade, Jove Ilica 154, Belgrade, Serbia.We prove a new fixed point theorem of order-Lipschitz mappings in Banach spaces without assumption of normalities of the
involving cones, which presents a positive answer to a problem raised in [S. Jiang, Z. Li, Fixed Point Theory Appl., 2016 (2016),
10 pages] and improves the corresponding results of Krasnoselskii and Zabreiko’s and Zhang and Sun’s since the normality of
the involving cone is removed.http://isr-publications.com/jnsa/3094/download-on-order-lipschitz-mappings-in-banach-spaces-without-normalities-of-involving-conesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110120170126Almost fixed point property for digital spaces associated with Marcus-Wyse topological spaces3447http://dx.doi.org/10.22436/jnsa.010.01.04ENSang-EonHanDepartment of Mathematics Education, Institute of Pure and Applied Mathematics, Chonbuk National University, Jeonju-City Jeonbuk, 54896, Republic of Korea.The present paper studies almost fixed point property for digital spaces whose structures are induced by Marcus-Wyse
(M-, for brevity) topology. In this paper we mainly deal with spaces X which are connected M-topological spaces withM-adjacency
(MA-spaces or M-topological graphs for short) whose cardinalities are greater than 1. Let MAC be a category whose objects,
denoted by Ob(MAC), are MA-spaces and morphisms are MA-maps between MA-spaces (for more details, see Section 3), and
MTC a category of M-topological spaces as Ob(MTC) and M-continuous maps as morphisms of MTC (for more details, see
Section 3). We prove that whereas any MA-space does not have the fixed point property (FPP for short) for any MA-maps, a
bounded simple MA-path has the almost fixed point property (AFPP for short). Finally, we refer the topological invariant of the
FPP for M-topological spaces from the viewpoint of MTC.http://isr-publications.com/jnsa/3095/download-almost-fixed-point-property-for-digital-spaces-associated-with-marcus-wyse-topological-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110120170126On the invariant measure of a piecewise-smooth circle homeomorphism of Zygmund class4859http://dx.doi.org/10.22436/jnsa.010.01.05ENSokhobiddinAkhatkulovSchool of Mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia, 43600 UKM Bangi, Selangor DE, Malaysia.Mohd. Salmi Md.NooraniSchool of Mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia, 43600 UKM Bangi, Selangor DE, Malaysia.HabibullaAkhadkulovSchool of Quantitative Sciences, University Utara Malaysia, CAS 06010, UUM Sintok, Kedah DA, Malaysia.We prove that the invariant probability measure of an orientation preserving circle homeomorphism f with several break
points (at which the derivative \(\acute{f}\) has jumps) is singular with respect to Lebesgue measure, if \(\acute{f}\) satisfies certain condition and
the product of jump ratios at break points is non-trivial. http://isr-publications.com/jnsa/3096/download-on-the-invariant-measure-of-a-piecewise-smooth-circle-homeomorphism-of-zygmund-classInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110120170126On a singular time-fractional order wave equation with Bessel operator and Caputo derivative 6070http://dx.doi.org/10.22436/jnsa.010.01.06ENSaidMesloubKing Saud University, College of Science, Mathematics Department, P. O. Box 2455, Riyadh 11451, Saudi Arabia.ImedBacharKing Saud University, College of Science, Mathematics Department, P. O. Box 2455, Riyadh 11451, Saudi Arabia.This paper deals with the study of the well-posedness of a mixed fractional problem for the wave equation defined in a
bounded space domain. The fractional time derivative is described in the Caputo sense. We prove the existence and uniqueness
of solution as well as its dependence on the given data. Our results develop and show the efficiency and effectiveness of the
functional analysis method when we deal with fractional partial differential equations instead of the nonfractional equations
which have been extensively studied by many authors during the last three decades.http://isr-publications.com/jnsa/3116/download-on-a-singular-time-fractional-order-wave-equation-with-bessel-operator-and-caputo-derivativeInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110120171126Sequential fractional differential equations and unification of anti-periodic and multi-point boundary conditions7183http://dx.doi.org/10.22436/jnsa.010.01.07ENAhmedAlsaediNonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia.BashirAhmadNonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia.MohammedAqlanNonlinear Analysis and Applied Mathematics (NAAM)-Research Group, Department of Mathematics, Faculty of Science, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia.In this paper, we present a novel idea of unification of anti-periodic and multi-point boundary conditions and develop the
existence theory for sequential fractional differential equations supplemented with these new conditions. We apply fixed point
theorems due to Banach, Krasnoselskii, Leray-Schauder alternative criterion, and Leray-Schauder degree theory to obtain the
desired results. Our results are well-illustrated with the aid of examples and correspond to some new special cases for particular
choices of parameters involved in the problem.http://isr-publications.com/jnsa/3117/download-sequential-fractional-differential-equations-and-unification-of-anti-periodic-and-multi-point-boundary-conditionsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110120170126Well-posedness for a class of strong vector equilibrium problems8491http://dx.doi.org/10.22436/jnsa.010.01.08ENYangYanlongSchool of computer science and technology, Guizhou University, Guiyang 550025, China.DengXicaiDepartment of Mathematics and Computer, Guizhou Normal College, Guiyang 550018, China.XiangShuwenSchool of computer science and technology, Guizhou University, Guiyang 550025, China.JiaWenshengSchool of computer science and technology, Guizhou University, Guiyang 550025, China.In this paper, we first construct a complete metric space \(\Lambda\) consisting of a class of strong vector equilibrium problems
(for short, (SVEP)) satisfying some conditions. Under the abstract framework, we introduce a notion of well-posedness for the
(SVEP), which unifies its Hadamard and Tikhonov well-posedness. Furthermore, we prove that there exists a dense \(G_{\delta}\) set Q of
\(\Lambda\) such that each (SVEP) in Q is well-posed, that is, the majority (in Baire category sense) of (SVEP) in \(\Lambda\) is well-posed. Finally,
metric characterizations on the well-posedness for the (SVEP) are given.http://isr-publications.com/jnsa/3118/download-well-posedness-for-a-class-of-strong-vector-equilibrium-problemsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110120170126\(\alpha\)-optimal best proximity point result involving proximal contraction mappings in fuzzy metric spaces92103http://dx.doi.org/10.22436/jnsa.010.01.09ENAbdulLatifDepartment of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi Arabia.NaeemSaleemDepartment of Mathematics, University of Management and Technology, C-II, Johar Town, Lahore - Pakistan.MujahidAbbasDepartment of Mathematics, University of Management and Technology, C-II, Johar Town, Lahore - Pakistan.In this paper, we introduce \(\alpha\)-proximal fuzzy contraction of type-I and II in complete fuzzy metric space and obtain some
fuzzy proximal and optimal coincidence point results. The obtained results further unify, extend and generalize some already
existing results in literature. We also provide some examples which show the validity of obtained results and a comparison is
also given which shows that contractive mappings and obtained results further generalizes already existing results in literature.http://isr-publications.com/jnsa/3119/download-alpha-optimal-best-proximity-point-result-involving-proximal-contraction-mappings-in-fuzzy-metric-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110120170126Quadratic \(\rho\)-functional inequalities in \(\beta\)-homogeneous normed spaces104110http://dx.doi.org/10.22436/jnsa.010.01.10ENYuanfengParkDepartment of Mathematics, Research Institute for Natural Sciences, Hanyang University, Seoul 133-791, Korea.YinhuaLuDepartment of Mathematics, School of Science, ShenYang University of Technology, Shenyang 110870, P. R. China.GangCuiDepartment of Mathematics, Yanbian University, Yanji 133001, P. R. China.ChoonkilJinDepartment of Mathematics, Yanbian University, Yanji 133001, P. R. China.In this paper, we solve the quadratic \(\rho\)-functional inequalities
\[\|f(x+y)+f(x-y)-2f(x)-2f(y)\|\leq\|\rho(4f(\frac{x+y}{2})+f(x-y)-2f(x)-2f(y))\|,\]
where \(\rho\) is a fixed complex number with \(|\rho|<1\), and\[\|4f(\frac{x+y}{2})+f(x-y)-2f(x)-2f(y)\|\leq\|\rho(f(x+y)+f(x-y)-2f(x)-2f(y))\|,\]
where \(\rho\) is a fixed complex number with \(|\rho|<1\).
Using the direct method, we prove the Hyers-Ulam stability of the quadratic \(\rho\)-functional inequalities (1) and (2) in \(\beta\)-
homogeneous complex Banach spaces.http://isr-publications.com/jnsa/3159/download-quadratic-rho-functional-inequalities-in-beta-homogeneous-normed-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110120170126Application of double Laplace decomposition method for solving singular one dimensional system of hyperbolic equations111121http://dx.doi.org/10.22436/jnsa.010.01.11ENHassan EltayebGadainMathematics Department, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia.In this paper, the Adomain decomposition methods and double Laplace transform methods are combined to study linear
and nonlinear singular one dimensional system of hyperbolic equations. In addition, we check the convergence of double
Laplace transform decomposition method applied to our problems. Furthermore, we illustrate our proposed methods by using
some examples.http://isr-publications.com/jnsa/3160/download-application-of-double-laplace-decomposition-method-for-solving-singular-one-dimensional-system-of-hyperbolic-equationsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110120170126Integral inequalities of extended Simpson type for (\(\alpha,m\))-varepsilon-convex functions122129http://dx.doi.org/10.22436/jnsa.010.01.12ENJunZhangCollege of Computer Science and Technology, Jilin University, Changchun 130012, China.Zhi-LiPeiCollege of Computer Science and Technology, Inner Mongolia University for Nationalities, Tongliao City, Inner Mongolia Autonomous Region, 028043, China.Gao-ChaoXuCollege of Computer Science and Technology, Jilin University, Changchun 130012, China.Xiao-HuiZouCollege of Computer Science and Technology, Jilin University, Changchun 130012, China.FengQiInstitute of Mathematics, Henan Polytechnic University, Jiaozuo City, Henan Province, 454010, China.In the paper, the authors establish some integral inequalities of extended Simpson type for \((\alpha,m)-\varepsilon\)-convex functions.http://isr-publications.com/jnsa/3174/download-integral-inequalities-of-extended-simpson-type-for-alpham-varepsilon-convex-functionsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110120170126The viscosity approximation forward-backward splitting method for solving quasi inclusion problems in Banach spaces130140http://dx.doi.org/10.22436/jnsa.010.01.13ENFu HaiZhaoSchool of Science, South West University of Science and Technology, Mianyang, Sichuan 621010, P. R. China.LiYangSchool of Science, South West University of Science and Technology, Mianyang, Sichuan 621010, P. R. China.In this paper, we introduce viscosity approximation forward-backward splitting method for an accretive operator and an
m-accretive operator in Banach spaces. The strong convergence of this viscosity method is proved under certain assumptions
imposed on the sequence of parameters. Applications to the minimization optimization problem and the linear inverse problem
are included. The results presented in the paper extend and improve some recent results announced in the current literature.http://isr-publications.com/jnsa/3175/download-the-viscosity-approximation-forward-backward-splitting-method-for-solving-quasi-inclusion-problems-in-banach-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110120170126Existence of mild solutions for a class of non-autonomous evolution equations with nonlocal initial conditions141153http://dx.doi.org/10.22436/jnsa.010.01.14ENTahiraJabeenAbdus Salam School of Mathematical Sciences, GC University, Lahore, Pakistan.VasileLupulescuConstantin Brancusi University, Republicii 1, 210152 Targu-Jiu, Romania.Using the techniques of measures of noncompactness and Schauder fixed point theorem, we present some existence results
for mild solutions of a class of nonlocal evolution equations involving causal operators. Moreover, we obtain the compactness
of the set of global mild solutions. An example is given to show the efficiency and usefulness of the results.http://isr-publications.com/jnsa/3199/download-existence-of-mild-solutions-for-a-class-of-non-autonomous-evolution-equations-with-nonlocal-initial-conditionsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110120170126Simultaneous iterative algorithm for the split equality fixed-point problem of demicontractive mappings154165http://dx.doi.org/10.22436/jnsa.010.01.15ENYaqinWangDepartment of Mathematics, Shaoxing University, Shaoxing 312000, China.Tae HwaKimDepartment of Applied Mathematics, College of Natural Sciences, Pukyong National University, Busan 48513, Republic of Korea.In this paper, we investigate a new simultaneous iterative algorithm for the split equality fixed-point problem of demicontractive
mappings in real Hilbert spaces and obtain a strong convergence result with no compactness assumptions on the spaces
or the mappings and with no extra conditions on the fixed point sets. The results obtained in this paper generalize and improve
the recent ones announced by many others.http://isr-publications.com/jnsa/3200/download-simultaneous-iterative-algorithm-for-the-split-equality-fixed-point-problem-of-demicontractive-mappingsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110120170127Multidimensional backward doubly stochastic differential equations with integral non-Lipschitz coefficients166174http://dx.doi.org/10.22436/jnsa.010.01.16ENPengjuDuanSchool of Mathematics and Statistics, Suzhou University, Anhui, 234000, China.The paper is devoted to solve multidimensional backward doubly stochastic differential equations under integral non-
Lipschitz conditions in general spaces. By stochastic analysis and constructing approximation sequence, a new set of sufficient
conditions for multidimensional backward doubly stochastic differential equations is obtained. The results generalize the recent
results on this issue. Finally, an example is given to illustrate the advantage of the main results.http://isr-publications.com/jnsa/3201/download-multidimensional-backward-doubly-stochastic-differential-equations-with-integral-non-lipschitz-coefficientsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110120170127On alternating direction method for solving variational inequality problems with separable structure175185http://dx.doi.org/10.22436/jnsa.010.01.17ENAbdellahBnouhachemLaboratoire d’Ingénierie des Systémes et Technologies de l’Information, ENSA, Ibn Zohr University, Agadir, BP 1136, Morocco.FatimazahraBenssiLaboratoire d’Ingénierie des Systémes et Technologies de l’Information, ENSA, Ibn Zohr University, Agadir, BP 1136, Morocco.AbdelouahedHamdiDepartment of Mathematics, Statistics and Physics College of Arts and Sciences, Qatar University, P. O. Box 2713, Doha, Qatar.We present an alternating direction scheme for the separable constrained convex programming problem. The predictor
is obtained via solving two sub-variational inequalities in a parallel wise at each iteration. The new iterate is obtained by a
projection type method along a new descent direction. The new direction is obtained by combining the descent directions using
by He [B.-S. He, Comput. Optim. Appl., 42 (2009), 195–212] and Jiang and Yuan [Z.-K. Jiang, X.-M. Yuan, J. Optim. Theory
Appl., 145 (2010), 311–323]. Global convergence of the proposed method is proved under certain assumptions. We also report
some numerical results to illustrate the efficiency of the proposed method.http://isr-publications.com/jnsa/3202/download-on-alternating-direction-method-for-solving-variational-inequality-problems-with-separable-structureInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110120170127Revisit of identities for Apostol-Euler and Frobenius-Euler numbers arising from differential equation186191http://dx.doi.org/10.22436/jnsa.010.01.18ENTaekyunKimDepartment of Mathematics, College of Science Tianjin Polytechnic University, Tianjin 300160, China.Gwan-WooJangDepartment of Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea.Jong JinSeoDepartment of Mathematics, Kwangwoon University, Seoul 139-701, Republic of Korea.In this paper, we study differential equation arising from the generating function of Apostol-Euler and Frobenius-Euler
numbers. In addition, we revisit some identities of Apostol-Euler and Frobenius-Euler numbers which are derived from differential
equations.http://isr-publications.com/jnsa/3203/download-revisit-of-identities-for-apostol-euler-and-frobenius-euler-numbers-arising-from-differential-equationInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110120170127Strong convergence of hybrid Bregman projection algorithm for split feasibility and fixed point problems in Banach spaces192204http://dx.doi.org/10.22436/jnsa.010.01.19ENJin-ZuoChenDepartment of Mathematics, Shanghai Normal University, Shanghai, 200234, China.Hui-YingHuDepartment of Mathematics, Shanghai Normal University, Shanghai, 200234, China.Lu-ChuanCengDepartment of Mathematics, Shanghai Normal University, Shanghai, 200234, China.In this paper, we consider and study split feasibility and fixed point problems involved in Bregman quasi-strictly pseudocontractive
mapping in Banach spaces. It is proven that the sequences generated by the proposed iterative algorithm converge
strongly to the common solution of split feasibility and fixed point problems.http://isr-publications.com/jnsa/3216/download-strong-convergence-of-hybrid-bregman-projection-algorithm-for-split-feasibility-and-fixed-point-problems-in-banach-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110120170127Hermite--Hadamard type inequalities for (\(\alpha,m\))-HA and strongly (\(\alpha,m\))-HA convex functions205214http://dx.doi.org/10.22436/jnsa.010.01.20ENChun-YingHeCollege of Mathematics, Inner Mongolia University for Nationalities, Tongliao City, Inner Mongolia Autonomous Region, China.YanWangCollege of Mathematics, Inner Mongolia University for Nationalities, Tongliao City, Inner Mongolia Autonomous Region, China.Bo-YanXiCollege of Mathematics, Inner Mongolia University for Nationalities, Tongliao City, Inner Mongolia Autonomous Region, China.FengQiInstitute of Mathematics, Henan Polytechnic University, Jiaozuo City, Henan Province, 454010, China.In the paper, the authors define the concepts of (\(\alpha,m\))-harmonic-arithmetically convex functions and strongly (\(\alpha,m\))-
harmonic-arithmetically convex functions, establish a new integral identity, and present some new Hermite–Hadamard type
inequalities for (\(\alpha,m\))-harmonic-arithmetically convex functions and strongly (\(\alpha,m\))-harmonic-arithmetically convex functions.
http://isr-publications.com/jnsa/3217/download-hermite-hadamard-type-inequalities-for-alpham-ha-and-strongly-alpham-ha-convex-functionsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110120170127Stochastic maximum principle for delayed backward doubly stochastic control systems215226http://dx.doi.org/10.22436/jnsa.010.01.21ENJieXuSchool of Mathematics, Jilin University, Changchun, 130012, China.YuecaiHanSchool of Mathematics, Jilin University, Changchun, 130012, China.In this paper, we investigate a class of doubly stochastic optimal control problems that the state trajectory is described
by backward doubly stochastic differential equations with time delay. By means of martingale representation theorem and
contraction mapping principle, the existence and uniqueness of solution for the delayed backward doubly stochastic differential
equation can be guaranteed. When the control domain is convex, we deduce a stochastic maximum principle as a necessary
condition of the optimal control by using classical variational technique. At the same time, under certain assumptions, a sufficient
condition of optimality is obtained by using the duality method. In the last section, we give the explicit form of the optimal
control for delayed doubly stochastic linear quadratic optimal control problem by our stochastic maximal principle.http://isr-publications.com/jnsa/3226/download-stochastic-maximum-principle-for-delayed-backward-doubly-stochastic-control-systemsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110120170127On completeness of root vectors of Schrödinger operators: a spectral approach227233http://dx.doi.org/10.22436/jnsa.010.01.22ENXiangdongYangDepartment of Mathematics, KunMing University of Science and Technology, 650093 KunMing,YunNan Province, China.We study complete properties of root vectors of Schrödinger operators. More accurately, denote by \(B(r_0)\) be the ball
centered at the origin with radius \(r_0\) and \(L^1(B(r_0))\) the space which consists of real functions f(x) satisfying
\(\int_{B(r_0)}|f(x)|dx<\infty\),
then the complete properties of eigenvectors for Schr¨odinger equation are characterized. Our characterization depends on the
sum of eigenvalues. Our proof is based on a complex-analytic conjugate approach which is widely used in the investigation of
completeness of function systems in Banach spaces.
http://isr-publications.com/jnsa/3227/download-on-completeness-of-root-vectors-of-schrodinger-operators-a-spectral-approachInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110120170127The approximation of solutions for second order nonlinear oscillators using the polynomial least square method234242http://dx.doi.org/10.22436/jnsa.010.01.23ENConstantinBotaDept. of Mathematics, Politehnica” University of Timişoara , P-ta Victoriei, 2, Timis¸oara, 300006, Romania.In this paper, polynomial least square method (PLSM) is applied to find approximate solution for nonlinear oscillator
differential equations. We illustrate that this method is very convenient and does not require linearization or small parameters.
Comparisons are made between the results of PLSM and other methods in order to prove the accuracy of the PLSM method.http://isr-publications.com/jnsa/3231/download-the-approximation-of-solutions-for-second-order-nonlinear-oscillators-using-the-polynomial-least-square-methodInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110120170127Existence and uniqueness of positive solutions for singular fractional differential systems with coupled integral boundary conditions243262http://dx.doi.org/10.22436/jnsa.010.01.24ENLishanLiuSchool of Mathematical Sciences, Qufu Normal University, 273165, Qufu, China.HongdanLiSchool of Mathematical Sciences, Qufu Normal University, 273165, Qufu, China.ChunLiuSchool of Mathematical Sciences, Qufu Normal University, 273165, Qufu, China.YonghongWuDepartment of Mathematics and Statistics, Curtin University, WA6845, Perth, Australia.In this paper, we study the existence and uniqueness of positive solutions for a class of singular fractional differential
systems with coupled integral boundary conditions. By using the properties of the Green function, the mixed monotone method
and the fixed point theory in cones, we obtain the existence and uniqueness results for the problem. The results obtained herein
generalize and improve some known results including singular and non-singular cases.http://isr-publications.com/jnsa/3251/download-existence-and-uniqueness-of-positive-solutions-for-singular-fractional-differential-systems-with-coupled-integral-boundary-conditionsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110120170127A modified iterative algorithm for finding a common element in Hilbert space263277http://dx.doi.org/10.22436/jnsa.010.01.25ENZhichuanZhuSchool of Statistics, Jilin University of Finance and Economics, Changchun, Jilin 130117, China.YanchunXingSchool of Statistics, Jilin University of Finance and Economics, Changchun, Jilin 130117, China.WeihuaDuanYatai School of Business Administration, Jilin University of Finance and Economics, Changchun, 130117, China.In this paper, a modified iterative algorithm for finding a common element of the solutions of a equilibrium problem, the
set of fixed points of nonexpansive mappings and the set of solutions of variational inequality problem is constructed in Hilbert
spaces, and the strong convergence of the generated iterative sequence to the common element is proved under some mild
conditions. The main result proposed in this paper extends and improves some recent results in the literature.http://isr-publications.com/jnsa/3263/download-a-modified-iterative-algorithm-for-finding-a-common-element-in-hilbert-spaceInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110120170127Application of the double Laplace Adomian decomposition method for solving linear singular one dimensional thermo-elasticity coupled system278289http://dx.doi.org/10.22436/jnsa.010.01.26ENHassanEltayebMathematics Department, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia.AdemKilicmanDepartment of Mathematics, University Putra Malaysia, 43400 Serdang, Selangor, Malaysia.SaidMesloubMathematics Department, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia.In the present work, the Adomain decomposition and double Laplace transform methods are combined to solve linear
singular one dimensional hyperbolic equation and linear singular one dimensional thermo-elasticity coupled system. Also we
address the convergence of double Laplace transform decomposition method. Moreover, some examples are given to establish
our method.http://isr-publications.com/jnsa/3271/download-application-of-the-double-laplace-adomian-decomposition-method-for-solving-linear-singular-one-dimensional-thermo-elasticity-coupled-systemInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110120170127The distributional Henstock-Kurzweil integral and applications II290298http://dx.doi.org/10.22436/jnsa.010.01.27ENWeiLiuCollege of Science, Hohai University, Nanjing 210098, P. R. China.GuojuYeCollege of Science, Hohai University, Nanjing 210098, P. R. China.DafangZhaoCollege of Science, Hohai University, Nanjing 210098, P. R. China.In this paper, we study a special Banach lattice \(D_{HK}\), which is induced by the distributional Henstock-Kurzweil integral,
and discuss its lattice properties. We show that \(D_{HK}\) is an AM-space with the Archimedean property and the Dunford-Pettis
property but it is not Dedekind complete. We also present two fixed point theorems in \(D_{HK}\). Meanwhile, two examples are
worked out to demonstrate the results.http://isr-publications.com/jnsa/3272/download-the-distributional-henstock-kurzweil-integral-and-applications-iiInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110120170127Solution of fractional oxygen diffusion problem having without singular kernel299307http://dx.doi.org/10.22436/jnsa.010.01.28ENBadr S.AlkahtaniMathematics Department, College of Science, King Saud University, Riyadh 11989, Saudi Arabia.Obaid J.AlgahtaniMathematics Department, College of Science, King Saud University, Riyadh 11989, Saudi Arabia.Ravi ShankerDubeyDepartment of Mathematics,Yagyavalkya Institute of Technology, Jaipur-302022, India.PranayGoswamiSchool of Liberal Studies, Ambedkar University Delhi, Delhi-11006, India.In the present paper, we use an efficient approach to solve fractional differential equation, oxygen diffusion problem which
is used to describe oxygen absorption in human body. The oxygen diffusion problem is considered in new Caputo derivative
of fractional order in this paper. Using an iterative approach, we derive the solutions of the modified system.http://isr-publications.com/jnsa/3273/download-solution-of-fractional-oxygen-diffusion-problem-having-without-singular-kernelInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110120170127Best proximity points of discontinuous operator in partially ordered metric spaces308315http://dx.doi.org/10.22436/jnsa.010.01.29ENB. S.ChoudhuryDepartment of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah-711103, West Bengal, India.M.JleliDepartment of Mathematics, College of Science, King Saud University, P. O. Box 2455, Riyadh 11451, Saudi Arabia.P.MaityDepartment of Mathematics, Indian Institute of Engineering Science and Technology, Shibpur, Howrah-711103, West Bengal, India.In this paper we establish best proximity point results for monotone multivalued mappings in partially ordered metric
spaces. We consider three notions of monotonicity of multivalued mappings. The main theorem is obtained by utilizing
property UC and MT-functions. There is no requirement of continuity on the multivalued function which is illustrated with two
supporting examples of the results established in this paper. There are two corollaries. Some existing results are extended to the
domain of partially ordered metric spaces through one of the corollaries.http://isr-publications.com/jnsa/3274/download-best-proximity-points-of-discontinuous-operator-in-partially-ordered-metric-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110120170127Some transcendence properties of integrals of Bessel functions316324http://dx.doi.org/10.22436/jnsa.010.01.30ENGulsahOnerDokuz Eylul University, 35210 ˙Izmir, Turkey.Mikhail V.NeschadimSobolev Institute of Mathematics and Novosibirsk State University, Novosibirsk, 630090, Russia.TahsinOnerDepartment of Mathematics, Ege University, 35100 ˙Izmir, Turkey.We prove that some integrals of Bessel functions are transcendence over ring of Bessel functions with coefficients from the
field of rational fractions of one variable.http://isr-publications.com/jnsa/3281/download-some-transcendence-properties-of-integrals-of-bessel-functionsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110120170127Controllability result of nonlinear higher order fractional damped dynamical system325337http://dx.doi.org/10.22436/jnsa.010.01.31ENJunpengLiuSchool of Mathematics, Jilin University, 130012, Changchun, P. R. China.SuliLiuSchool of Mathematics, Jilin University, 130012, Changchun, P. R. China.HuilaiLiSchool of Mathematics, Jilin University, 130012, Changchun, P. R. China.In this paper, we investigate the controllability of nonlinear fractional damped dynamical system, which involved fractional
Caputo derivatives of any different orders. In the process of proof, we mainly use the Schaefer’s fixed-point theorem and
Mittag-Leffler matrix function. At last, we give an example to illustrate our main result.http://isr-publications.com/jnsa/3282/download-controllability-result-of-nonlinear-higher-order-fractional-damped-dynamical-system