International Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170806Fixed point theorems in modular vector spaces40464057http://dx.doi.org/10.22436/jnsa.010.08.01ENA. A. N.Abdou M. A.Khamsi In this work, we initiate the metric fixed point theory in modular vector spaces under Nakano formulation. In particular, we establish an analogue to Banach contraction principle, Browder and Gohde fixed point theorems for nonexpansive mappings in the modular sense. Then we finish by proving a common fixed point result of a commutative family of nonexpansive mappings in the modular sense.
http://isr-publications.com/jnsa/5185/download-fixed-point-theorems-in-modular-vector-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170806Skew cyclic displacements and decompositions of inverse matrix for an innovative structure matrix40584070http://dx.doi.org/10.22436/jnsa.010.08.02ENX.Jiang K.Hong Z.Fu In this paper, we study mainly on a class of column upper-minus-lower (CUML) Toeplitz matrices without standard Toeplitz structure, which are `` similar'' to the Toeplitz matrices. Their (-1,-1)-cyclic displacements coincide with cyclic displacement of some standard Toeplitz matrices. We obtain the formula on representation for the inverses of CUML Toeplitz matrices in the form of sums of products of (-1, 1)-circulants and (1, -1)-circulants factor by constructing the corresponding displacement of the matrices. In addition, based on the relation between CUML Toeplitz matrices and CUML Hankel matrices, the inverse formula of CUML Hankel matrices can also be obtained.
http://isr-publications.com/jnsa/5186/download-skew-cyclic-displacements-and-decompositions-of-inverse-matrix-for-an-innovative-structure-matrixInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170806On approximate homomorphisms of ternary semigroups40714076http://dx.doi.org/10.22436/jnsa.010.08.03ENK.CieplińskiWe prove the generalized Ulam stability of ternary homomorphisms from commutative ternary semigroups into \(n\)-Banach spaces as well as into complete non-Archimedean normed spaces. Ternary algebraic structures appear in various domains of theoretical and mathematical physics, and \(p\)-adic numbers, which are the most important examples of non-Archimedean fields, have gained the interest of physicists for their research in some problems coming from quantum physics, \(p\)-adic strings and superstrings.
http://isr-publications.com/jnsa/5187/download-on-approximate-homomorphisms-of-ternary-semigroupsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170806On the generalized solutions of a certain fourth order Euler equations40774084http://dx.doi.org/10.22436/jnsa.010.08.04ENA.Liangprom K.Nonlaopon In this paper, using Laplace transform technique, we propose the generalized solutions of the fourth order Euler differential equations \[t^4y^{(4)}(t)+t^3y'''(t)+t^2y''(t)+ty'(t)+my(t)=0,\] where \(m\) is an integer and \(t\in\mathbb{R}\). We find types of solutions depend on the values of \(m\). Precisely, we have a distributional solution for \(m=-k^4-5k^3-9k^2-4k\) and a weak solution for \(m=-k^4+5k^3-9k^2+4k,\) where \(k\in\mathbb{N}.\)
http://isr-publications.com/jnsa/5188/download-on-the-generalized-solutions-of-a-certain-fourth-order-euler-equationsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170807On some common coupled fixed point results in rectangular \(b\)-metric spaces40854098http://dx.doi.org/10.22436/jnsa.010.08.05ENFengGu In this paper, by using the \(w\)-compatible conditions of mapping pair, we discuss the existence and uniqueness problem of the common coupled fixed point for mappings defined on a set equipped with two rectangular \(b\)-metrics. Some new common coupled fixed point theorems are obtained. We also provide
illustrative examples in support of our new results. As application, we provide an existence and uniqueness theorem of common solution for a class of nonlinear integral equations by using the obtained new result. The results presented in this paper generalize the well-known comparable results in the literature.
http://isr-publications.com/jnsa/5195/download-on-some-common-coupled-fixed-point-results-in-rectangular-b-metric-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170807Weak convergence of an iterative algorithm for accretive operators 40994108http://dx.doi.org/10.22436/jnsa.010.08.06ENH.Zhao S. Y.Cho In this paper, an iterative algorithm investigated for \(m\)-accretive and inverse-strongly accretive operators. Also, a weak convergence theorem for the sum of two accretive operators is established in a real uniformly convex and \(q\)-uniformly
smooth Banach space.http://isr-publications.com/jnsa/5196/download-weak-convergence-of-an-iterative-algorithm-for-accretive-operatorsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170807Relaxed inertial accelerated algorithms for solving split equality feasibility problem41094121http://dx.doi.org/10.22436/jnsa.010.08.07ENM. X.Li X. P.Kao H. T.CheIn this paper, we study the split equality feasibility problem and present two algorithms for solving the problem with special structure. We prove the weak convergence of these algorithms under mild conditions. Especially, the selection of stepsize is only dependent on the information of current iterative points, but independent from the prior knowledge of operator norms. These algorithms provide new ideas for solving the split equality feasibility problem. Numerical results demonstrate the feasibility and effectiveness of these algorithms.
http://isr-publications.com/jnsa/5197/download-relaxed-inertial-accelerated-algorithms-for-solving-split-equality-feasibility-problemInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170809Second-order accurate numerical approximations for the fractional percolation equations41224136http://dx.doi.org/10.22436/jnsa.010.08.08ENX.Yin L.Li S.FangFirst, we examine a practical numerical method which based on the classical Crank-Nicholson (CN) method combined with Richardson extrapolation is used to solve a class of one-dimensional initial-boundary value fractional percolation equation (FPE) with variable coefficients on a finite domain. Secondly, we present ADI-CN method for the two-dimensional fractional percolation equation. Stability and convergence of these methods are proved. Using these methods, we can achieve second-order convergence in time and space. Finally, numerical examples are presented to verify the order of convergence.
http://isr-publications.com/jnsa/5208/download-second-order-accurate-numerical-approximations-for-the-fractional-percolation-equationsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170809Some identities of \(\lambda\)-Daehee polynomials41374142http://dx.doi.org/10.22436/jnsa.010.08.09ENJ. G.Lee J. K.Kwon G.-W.Jang L.-C.JangIn this paper, we give some identities of \(\lambda\)-Daehee polynomials and investigate a new and interesting identities of \(\lambda\)-Daehee polynomial arising from the symmetry properties of the \(p\)-adic invariant integral on \(\mathbb{Z}_p\).http://isr-publications.com/jnsa/5209/download-some-identities-of-lambda-daehee-polynomialsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170810Convergence analysis of a Halpern-like iterative algorithm in Hilbert spaces41434149http://dx.doi.org/10.22436/jnsa.010.08.10ENY.Zhang S. Y.Cho In this paper, a Halpern-like iterative algorithm is investigated for finding a solution of a split feasibility problem and a solution to a nonexpansive operator equation. Strong convergence theorems are established in the framework of infinite dimensional Hilbert spaces.
http://isr-publications.com/jnsa/5226/download-convergence-analysis-of-a-halpern-like-iterative-algorithm-in-hilbert-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170810Some properties and mappings on weakly \(\nu \)-Lindelöf generalized topological spaces41504161http://dx.doi.org/10.22436/jnsa.010.08.11ENM.Abuage A.Kılıçman Our work aims to study weakly \(\nu \)-Lindelöf (briefly \(w\nu \)-Lindelöf) space in generalized topological spaces. Some characterizations of \(w\nu \)-Lindelöf subspaces and subsets are showed.
Furthermore, we shall show that the \(w\nu \)-Lindelöf generalized topological space is not a hereditary property. Finally, the effect of some mappings and decompositions of continuity are studied. The main result that we obtained on is the effect of almost \((\nu, \mu)\)-continuous function on \(w\nu \)-Lindelöf generalized topological space.
http://isr-publications.com/jnsa/5228/download-some-properties-and-mappings-on-weakly-nu-lindelof-generalized-topological-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170811Some applications with new admissibility contractions in \(b\)-metric spaces41624174http://dx.doi.org/10.22436/jnsa.010.08.12ENL.Paunović P.Kaushik S.KumarThe work presented in this paper extends the idea of \(\alpha-\beta\)-contractive mappings in the framework of \(b\)-metric spaces. Fixed points are investigated for such kind of mappings. An example is given to show the superiority of our results. As applications we discuss Ulam-Hyres stability, well-posedness
and limit shadowing of fixed point problem.
http://isr-publications.com/jnsa/5230/download-some-applications-with-new-admissibility-contractions-in-b-metric-spacesInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170811Lie group method and fractional differential equations41754180http://dx.doi.org/10.22436/jnsa.010.08.13ENM. M.Alshamrani H. A.Zedan M.Abu-NawasIn this paper, Lie group method is applied to investigate and solve
some classes of nonlinear fractional differential equations. In
addition, we use the obtained symmetries to induce exact solutions for the equations under consideration.
http://isr-publications.com/jnsa/5231/download-lie-group-method-and-fractional-differential-equationsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170813Hopf bifurcation analysis and its preliminary control in a Hasting-Powell food chain model with two different delays41814196http://dx.doi.org/10.22436/jnsa.010.08.14ENJ. G.Zhang J. R.Lu W. J.Du Y. D.Chu H. W.LuoKeeping the balance of nature is important, and it is very significant to effectively control the number of species for ecosystem stability. In this paper, we propose a tritrophic Hastings-Powell (HP) model with two different time delays, and the local stability of equilibrium, Hopf bifurcation, and the existence and uniqueness of the positive equilibrium are analyzed in detail. Besides, we obtain the stable conditions for the system and prove that Hopf bifurcation will occur when the delay pass through the critical value. And the stability and direction of the Hopf bifurcation are also investigated by using the center manifold theorem and normal form theorem. Finally, some numerical examples are given to illustrate the results.
http://isr-publications.com/jnsa/5254/download-hopf-bifurcation-analysis-and-its-preliminary-control-in-a-hasting-powell-food-chain-model-with-two-different-delaysInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170813Fixed point results for generalized \((\alpha-\eta)-\Theta\) contractions with applications41974208http://dx.doi.org/10.22436/jnsa.010.08.15ENN.Hussain A. E.Al-Mazrooei J.Ahmad The aim of this paper is to define
generalized \((\alpha-\eta)-\Theta\) contraction and to extend the results of Jleli and Samet [M. Jleli, B. Samet, J. Inequal. Appl., \(\bf{2014}\) (2014), 8 pages] by applying a simple condition on the function \(\Theta\). We also deduce certain fixed and
periodic point results for orbitally continuous generalized \(\Theta \)-contractions and certain fixed point results for integral inequalities are derived. Finally, we provide an example to show the significance of the
investigation of this paper.
http://isr-publications.com/jnsa/5256/download-fixed-point-results-for-generalized-alpha-eta-theta-contractions-with-applicationsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170816Global well-posedness of strong solution for the three dimensional dynamic Cahn-Hilliard-Stokes model42094221http://dx.doi.org/10.22436/jnsa.010.08.16ENK. L.Cheng W. Q.Feng The global well-posedness analysis for the three dimensional dynamic Cahn-Hilliard-Stokes (CHS) model is provided in this paper. In this model, the velocity vector is determined by the phase variable by both the Darcy law and the Stokes equation. Based on the analysis of weak solutions to the CHS equation by the standard Galerkin method, we present a global in time strong solution for the CHS model. Moreover, the existence and the uniqueness of the strong solution are also proven.
http://isr-publications.com/jnsa/5280/download-global-well-posedness-of-strong-solution-for-the-three-dimensional-dynamic-cahn-hilliard-stokes-modelInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170816Optimal harvesting policy of a stochastic delay predator-prey model with Lévy jumps42224230http://dx.doi.org/10.22436/jnsa.010.08.17ENM.DengThis paper considers the optimal harvesting of a stochastic delay predator-prey model with Lévy jumps. The traditional optimal harvesting problem of this type of model is difficult because it is difficult to get the explicit solutions of the model or to solve the corresponding delay Fokker-Planck equation of the model. In this paper, we use an ergodic method to study this problem, and establish the sufficient and necessary conditions for the existence of an optimal harvesting strategy of the model. In addition, we gain the explicit forms of the optimal harvesting effort and the maximum of the cost function. One can see that the ergodic method used in this paper can avoid solving both the model and the corresponding delay Fokker-Planck equation.
http://isr-publications.com/jnsa/5281/download-optimal-harvesting-policy-of-a-stochastic-delay-predator-prey-model-with-levy-jumpsInternational Scientific Research PublicationsJournal of Nonlinear Sciences and Applications(JNSA)ISSN 2008-190110820170816New numerical analysis of Riemann-Liouville time-fractional Schrödinger with power, exponential decay, and Mittag-Leffler laws42314243http://dx.doi.org/10.22436/jnsa.010.08.18ENB. S. T.Alkahtani I.Koca A.Atangana The mathematical equation that describes how the quantum state of a quantum system changes during time was considered within the framework of fractional differentiation with three
different derivatives in Riemann-Liouville sense. The fractional derivatives used in this work are constructed based on power, exponential decay, and Mittag-Leffler law. A new numerical scheme for fractional derivative in Riemann-Liouville sense is presented and used to solve numerically the Schrödinger equation. The stability analysis of each model is presented in
detail.
http://isr-publications.com/jnsa/5282/download-new-numerical-analysis-of-riemann-liouville-time-fractional-schrodinger-with-power-exponential-decay-and-mittag-leffler-laws