International Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101220171202Some new integral inequalities for \(n\)-times differentiable convex and concave functions61416148http://dx.doi.org/10.22436/jnsa.010.12.01ENSelahattin MadenDepartment of Mathematics, Faculty of Sciences and Arts, Ordu University-Ordu-TurkeyHuriye KadakalInstitute of Science, Ordu University-Ordu-TurkeyMahir KadakalDepartment of Mathematics, Faculty of Sciences and Arts, Giresun University-Giresun-Turkey İmdatİscanDepartment of Mathematics, Faculty of Sciences and Arts, Giresun University-Giresun-TurkeyIn this work, by using an integral identity together with both the Holder and the Power-mean integral inequalities we establish several new inequalities for \(n\)-times differentiable convex and concave mappings.http://isr-publications.com/jnsa/6305/download-some-new-integral-inequalities-for-n-times-differentiable-convex-and-concave-functionsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101220171202Wavelet thresholding estimator on \(B_{p,q}^s(\mathbb{R}^n)\)61496158http://dx.doi.org/10.22436/jnsa.010.12.02ENJunjian ZhaoDepartment of Mathematics, School of Science, Tianjin Polytechnic University, Tianjin 300387, ChinaZhitao ZhuangSchool of Mathematics and Information Sciences, North China University of Water Resources and Electric Power, Zhengzhou 450011, ChinaThis paper deals with the convergence of the wavelet thresholding estimator on Besov spaces \(B_{p,q}^s(\mathbb{R}^n)\). We show firstly the equivalence of several Besov norms. It seems different with one dimensional case. Then we provide two convergence theorems for the wavelet thresholding estimator, which extend Liu and Wang's work [Y.-M. Liu, H.-Y. Wang, Appl. Comput. Harmon. Anal., \({\bf 32}\) (2012), 342--356]. http://isr-publications.com/jnsa/6306/download-wavelet-thresholding-estimator-on-b-pqsmathbbrnInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101220171202On some extensions of Nadler's fixed point theorem61596165http://dx.doi.org/10.22436/jnsa.010.12.03ENNajeh RedjelLaboratory of Informatics and Mathematics, University of Souk-Ahras, P. O. Box 1553 Souk-Ahras 41000, AlgeriaAbdelkader DehiciLaboratory of Informatics and Mathematics, University of Souk-Ahras, P. O. Box 1553 Souk-Ahras 41000, AlgeriaIn this paper, we give the notion of the pseudo-fixed point for multi-valued mappings which enable us to extend Nadler's theorem and other well-known results in the literature.http://isr-publications.com/jnsa/6307/download-on-some-extensions-of-nadlers-fixed-point-theoremInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101220171202Inequalities for new class of fractional integral operators61666176http://dx.doi.org/10.22436/jnsa.010.12.04ENHasib KhanCollege of Engineering, Mechanics and Materials, Hohai University, 211100, Nanjing, P. R. ChinaHongguang SunCollege of Engineering, Mechanics and Materials, Hohai University, 211100, Nanjing, P. R. ChinaWen ChenCollege of Engineering, Mechanics and Materials, Hohai University, 211100, Nanjing, P. R. ChinaDumitru BaleanuDepartment of Mathematics, Cankaya University, 06530 Ankara, TurkeyThe applications of fractional order integrals have promoted the study of inequalities. In this paper, we utilize recently introduced left- and right-fractional conformable integrals (FCI) for a class of decreasing \(n\) positive functions such that \(n\in N\), for the generalization of existing integral inequalities. Our results have the potentials to be used for the investigation of positive solutions of different classes of fractional differential equations.http://isr-publications.com/jnsa/6308/download-inequalities-for-new-class-of-fractional-integral-operatorsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101220171206Permanence and partial extinction in a delayed three-species food chain model with stage structure and time-varying coefficients61776191http://dx.doi.org/10.22436/jnsa.010.12.05ENHuanyanXiDepartment of Mathematics and Statistics, Changsha University of Science and Technology, 410114, Changsha, P. R. ChinaLihongHuangDepartment of Mathematics and Statistics, Changsha University of Science and Technology, 410114, Changsha, P. R. ChinaYunchengQiaoDepartment of Mathematics and Statistics, Changsha University of Science and Technology, 410114, Changsha, P. R. ChinaHuaiyuLiDepartment of Mathematics and Statistics, Changsha University of Science and Technology, 410114, Changsha, P. R. ChinaChuangxiaHuangDepartment of Mathematics and Statistics, Changsha University of Science and Technology, 410114, Changsha, P. R. ChinaBy taking full consideration of maturity (\(\tau_{1}\) represents the maturity of predator and \(\tau_{2}\) represents the maturity of top predator)
and the effects of environmental parameters, a new delayed three-species food chain model with stage structure and time-varying coefficients is
established. With the help of the comparison theorem and the technique of mathematical analysis, the positivity and boundedness of solutions of
the model are investigated. Furthermore, some sufficient conditions on the permanence and partial extinction of the system are derived.
Some interesting findings show that the delays have great impacts on the permanence for the system. More precisely, if \(\tau_{2}\in(n, +\infty)\),
then the system is partially extinct: on one hand, if \(\tau_{1}\in(0,n_{1})\) and \(\tau_{2}\in(n, +\infty)\), then the prey and predator species
will coexist, i.e., both the prey and predator species are always permanent, yet the top predator species will go extinct eventually.
On the other hand, if \(\tau_{1}\in(n_{4},+\infty)\) and \(\tau_{2}\in(n, +\infty)\), where \(n_{4}\) is greater than \(n_{1}\),
then all predator species will become extinct eventually. Numerical simulations are great well agreement with the theoretical results.http://isr-publications.com/jnsa/6346/download-permanence-and-partial-extinction-in-a-delayed-three-species-food-chain-model-with-stage-structure-and-time-varying-coefficientsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101220171206Common fixed points for pairs of triangular \(\alpha\)-admissible mappings61926204http://dx.doi.org/10.22436/jnsa.010.12.06ENHaitham QawagnehSchool of mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia, 43600 UKM, Selangor Darul Ehsan, MalaysiaMohd Salmi MD NooraniSchool of mathematical Sciences, Faculty of Science and Technology, University Kebangsaan Malaysia, 43600 UKM, Selangor Darul Ehsan, MalaysiaWasfi ShatanawiDepartment of Mathematics and General Courses, Prince Sultan University, Riyadh, Saudi ArabiaHabes AlsamirDepartment of Mathematics and General Courses, Aljouf University, Aljouf, Saudi ArabiaIn this paper, we introduce the notation of \((\alpha-\eta)-(\psi-\varphi)\)-contraction mappings defined on a set \(X\).
We prove the existence of common fixed point results for the pair of self-mappings involving C-class functions in the
setting of metric space. Our results generalize and extend several works existing in literature. We provide an example
and some applications in order to support our results.http://isr-publications.com/jnsa/6347/download-common-fixed-points-for-pairs-of-triangular-alpha-admissible-mappingsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101220171206Dynamics of a stochastic service-resource mutualism model with Lévy noises and harvesting62056218http://dx.doi.org/10.22436/jnsa.010.12.07ENHui WangSchool of Mathematical Science, Huaiyin Normal University, Huaian 223300, P. R. ChinaChenxi DuSchool of Mathematical Science, Huaiyin Normal University, Huaian 223300, P. R. ChinaMeng LiuSchool of Mathematics and Statistics, Northeast Normal University, Jilin 130024, P. R. ChinaIn this paper, we propose a stochastic service-resource mutualism model with Lévy noises and harvesting. Under some assumptions, we study several dynamical properties of the model. We first obtain the thresholds between persistence and extinction for both the service species and the resource species. Then we give sharp sufficient conditions for stability in distribution of the model. Finally, we establish sufficient and necessary criteria for the existence of the optimal harvesting policy. The optimal harvesting effort and maximum of sustainable yield are also obtained. Our results reveal that the persistence, extinction, stability in distribution and optimal harvesting strategy have close relationships with the random noises.http://isr-publications.com/jnsa/6349/download-dynamics-of-a-stochastic-service-resource-mutualism-model-with-levy-noises-and-harvestingInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101220171206Identities of the degenerate Daehee numbers with the Bernoulli numbers of the second kind arising from nonlinear differential equation62196228http://dx.doi.org/10.22436/jnsa.010.12.08ENSung-Soo PyoDepartment of Mathematics Education, Silla University, Busan, Rep. of KoreaTaekyun KimDepartment of Mathematics, Kwangwoon University, Seoul, Rep. of KoreaSeog-Hoon RimDepartment of Mathematics Education, Kyungpook National University, Taegu, Rep. of KoreaIn [T. Kim, D. S. Kim, H. I. Kwon, J. J. Seo, Glob. J. Pure Appl. Math., \({\bf 12}\) (2016), 1893--1901], Kim et al. presented some identities for the
Bernoulli numbers of the second kind using differential equation.
Here we use this differential equation in a different way. In this
paper, we deduce some identities of the degenerate Daehee numbers
with the Bernoulli numbers of the second kind of order \(r\).http://isr-publications.com/jnsa/6350/download-identities-of-the-degenerate-daehee-numbers-with-the-bernoulli-numbers-of-the-second-kind-arising-from-nonlinear-differential-equationInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101220171206Existence and multiplicity of periodic solutions and subharmonic solutions for a class of elliptic equations62296245http://dx.doi.org/10.22436/jnsa.010.12.09ENXiujuan WangSchool of Mathematical Sciences, Qufu Normal University, Shandong 273165, P. R. ChinaAixia QianSchool of Mathematical Sciences, Qufu Normal University, Shandong 273165, P. R. ChinaThis paper focuses on the following elliptic equation
\[
\left\{ \begin{aligned}
& -u''- p(x)u=f(x,u),\quad \text{a.e.}\quad x\in[0,l],\\
&u(0)-u(l)=u'(0)-u'(l)=0,
\end{aligned} \right. \]
where the primitive function of \(f(x,u)\) is either superquadratic or asymptotically quadratic as \(|u|\rightarrow\infty\), or subquadratic as \(|u|\rightarrow0\). By using variational method, e.g. the local linking theorem, fountain theorem, and the generalized mountain pass theorem, we establish the existence and multiplicity results for the periodic solution and subharmonic solution.http://isr-publications.com/jnsa/6351/download-existence-and-multiplicity-of-periodic-solutions-and-subharmonic-solutions-for-a-class-of-elliptic-equationsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101220171206An LQP-SQP alternating direction method for solving variational inequality problems with separable structure62466261http://dx.doi.org/10.22436/jnsa.010.12.10ENAdnan AlhomaidanDepartment of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi ArabiaAbdellah BnouhachemLaboratoire d'Ingénierie des Systèmes et Technologies de l'Information, Ibn Zohr University, Agadir, BP 1136, MoroccoAbdul LatifDepartment of Mathematics, King Abdulaziz University, P. O. Box 80203, Jeddah 21589, Saudi ArabiaIn this paper, by combining the
logarithmic-quadratic proximal (LQP) method and the square
quadratic proximal (SQP) method, we propose an inexact
alternating direction method for solving constrained variational
inequalities \(VI(S,f),\) where \(S\) is a convex set with linear
constraints.
Under certain conditions, the global
convergence of the proposed method is established. We show the
O(1/t) convergence rate for the inexact LQP-SQP alternating
direction method. To demonstrate the efficiency of the proposed
method, we provide numerical results for traffic equilibrium
problems.http://isr-publications.com/jnsa/6352/download-an-lqp-sqp-alternating-direction-method-for-solving-variational-inequality-problems-with-separable-structureInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101220171209Invariance analysis and exact solutions of some sixth-order difference equations62626273http://dx.doi.org/10.22436/jnsa.010.12.11ENDarlison NyirendaSchool of Mathematics, University of the Witwatersrand, 2050, Johannesburg, South AfricaMensah Folly-GbetoulaSchool of Mathematics, University of the Witwatersrand, 2050, Johannesburg, South AfricaWe perform a full Lie point symmetry analysis of difference equations of the form
\[
u_{n+6}=\frac{u_nu_{n+4}}{u_{n+2}(A _n + B _n u_nu_{n+4})}\ ,
\]
where the initial conditions are non-zero real numbers. Consequently, we obtain four non-trivial symmetries. Eventually, we get solutions of the difference equation for random sequences \((A_n)\) and \((B_n)\). This work is a generalization of a recent result by Khaliq and Elsayed [A. Khaliq, E. M. Elsayed, J. Nonlinear Sci. Appl., \({\bf 9}\) (2016), 1052--1063].http://isr-publications.com/jnsa/6374/download-invariance-analysis-and-exact-solutions-of-some-sixth-order-difference-equationsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101220171209On the existence of generalized weak solutions to discontinuous fuzzy differential equations62746287http://dx.doi.org/10.22436/jnsa.010.12.12ENYa-Bin ShaoSchool of Science, Chongqing University of Posts and Telecommunications, 400065 Nanan, Chongqing, People's Republic of ChinaZeng-Tai GongCollege of Mathematics and Statistics, Northwest Normal University, 730070 Lanzhou, Gansu, People's Republic of ChinaZi-Zhong ChenCollege of Computer Science and Technology, Chongqing University of Posts and Telecommunications, 400065 Nanan, Chongqing, People's Republic of ChinaIn this paper, by means of replacing the Lebesgue integrability of
support functions with its Henstock integrability, the definitions of the Henstock-Pettis integral of \(n\)-dimensional fuzzy-number-valued
functions are defined. In addition, the controlled convergence theorems for such
integrals are considered. As the applications of these integrals,
we provide some existence theorems of generalized weak solutions to initial value problems for the discontinuous fuzzy differential equations under the strong GH-differentiability.http://isr-publications.com/jnsa/6375/download-on-the-existence-of-generalized-weak-solutions-to-discontinuous-fuzzy-differential-equationsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101220171209Periodic problem of first order nonlinear uncertain dynamic systems62886297http://dx.doi.org/10.22436/jnsa.010.12.13ENYongzhao WangSchool of Mathematics and Statistics, Anyang Normal University, Anyang, 455000, ChinaQian LiuSchool of Civil Engineering and Architecture, Anyang University, Anyang, 455000, ChinaQiansheng FengFaculty of Mathematics and Physics, Huaiyin Institute of Technology, Huaian, 223003, ChinaThe solution to fuzzy differential equation
is very important for solving the uncertainly practical problems in the real world.
In this paper, the definition of solution for periodic problems of
fuzzy differential equations based on the theory of differential inclusions is given.
Using the theory of differential inclusions, function analysis and
Kakutani Fixed point theorem, an existence theorem of periodic solutions to first order uncertain
dynamical systems is obtained in a more general set.http://isr-publications.com/jnsa/6376/download-periodic-problem-of-first-order-nonlinear-uncertain-dynamic-systemsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101220171213A new iterative scheme in CAT(0) spaces with convergence analysis62986310http://dx.doi.org/10.22436/jnsa.010.12.14ENG. S. SalujaDepartment of Mathematics, Govt. Kaktiya P. G. College, Jagdalpur, Jagdalpur - 494001 (C.G.), IndiaAdrian GhiuraUniversity Politehnica of Bucharest, Bucharest, RomaniaMihai PostolacheChina Medical University, Taichung, TaiwanIn this paper, we establish strong and \(\Delta\)-convergence theorems
in CAT\((0)\) spaces for two total asymptotically nonexpansive non-self
mappings via a new two-step iterative scheme for non-self-mappings.
Our results extend and generalize several results from the current
existing literature.http://isr-publications.com/jnsa/6403/download-a-new-iterative-scheme-in-cat0-spaces-with-convergence-analysisInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101220171213On the mechanism of integration of informatization and industrialization based on dynamics of stochastic model63116323http://dx.doi.org/10.22436/jnsa.010.12.15ENChaodong YanCollege of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, ChinaJing MaCollege of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, ChinaDandan LiCollege of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, ChinaIn recent years, with the new generation of information and communication technology in the industrial field more widely used, the integration of informatization and industrialization aroused people's research and attention again. The connotation and mechanism of integration of informatization and industrialization is one of the focuses of people's research. In this paper, a stochastic model that describes the interaction between information and industrial technology is proposed and analyzed. Sharp sufficient conditions for increase and stagnate of the diffusion rates for both information and industrial technology are established. The results reveal that the stochastic perturbations can affect the dynamics of model significantly.http://isr-publications.com/jnsa/6404/download-on-the-mechanism-of-integration-of-informatization-and-industrialization-based-on-dynamics-of-stochastic-modelInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101220171213Classifications and duality relations for several integral transforms63246332http://dx.doi.org/10.22436/jnsa.010.12.16ENXin LiangState Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, ChinaFeng GaoSchool of Mechanics and Civil Engineering, China University of Mining and Technology, Xuzhou 221116, ChinaShan-Jie SuState Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, ChinaZhen WangCollege of Mathematics and Systems Science, Shandong University of Science and Technology, Qingdao 266590, ChinaXiao-Jun YangState Key Laboratory for Geomechanics and Deep Underground Engineering, China University of Mining and Technology, Xuzhou 221116, ChinaIn this paper, we classify several integral transforms into two
categories according to the types of their kernel functions and two novel
definitions of general integral transforms are suggested. Based on the general integral transforms, some of their
basic properties are proved. In addition, the dualities between those
two kinds of integral transforms are deducted and discussed in detail. The interesting
coupling relations in symmetric form is illustrated graphically. The
analysis shows that the classifications are reasonable and the dualities are
significant.http://isr-publications.com/jnsa/6405/download-classifications-and-duality-relations-for-several-integral-transformsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-1901101220171213Multiple positive solutions of fractional-order boundary value problem with integral boundary conditions63336343http://dx.doi.org/10.22436/jnsa.010.12.17ENYouyu WangDepartment of Mathematics, Tianjin University of Finance and Economics, Tianjin 300222, P. R. ChinaShuilian LiangDepartment of Mathematics, Tianjin University of Finance and Economics, Tianjin 300222, P. R. ChinaQichao WangDepartment of Mathematics, Tianjin University of Finance and Economics, Tianjin 300222, P. R. ChinaWe concentrate on investigating the existence of positive solutions
for fractional-order differential equations with integral conditions
in this article. The problem is issued by applying Avery-Peterson
fixed-point theorem and the properties of Green's function. At the
same time, we provide an example to make our results clear and easy
for readers' to understand the multiplicity of solutions.http://isr-publications.com/jnsa/6406/download-multiple-positive-solutions-of-fractional-order-boundary-value-problem-with-integral-boundary-conditions