Current Issue : July - September Volume : 2019 Issue Number : 3 Articles : 6 Articles
The aim of this paper is to prove the existence and uniqueness of points of coincidence and common fixed points for a pair of\nself-mappings defined on generalized metric spaces with a graph. Our results improve and extend several recent results of metric\nfixed point theory....
The purpose of this brief article is to initiate discussions in this special issue by proposing\ndesiderata for calling an operator a fractional derivative or a fractional integral. Our desiderata are\nneither axioms nor do they define fractional derivatives or integrals uniquely. Instead they intend\nto stimulate the field by providing guidelines based on a small number of time honoured and well\nestablished criteria....
This paper addresses the present day problem of multiple proposals for operators under\nthe umbrella of â??fractional derivativesâ?. Several papers demonstrated that various of those â??novelâ?\ndefinitions are incorrect. Here the classical system theory is applied to develop a unified framework\nto clarify this important topic in Fractional Calculus....
In this paper, we study a class of nonlinear Choquard equation driven by the fractional\nLaplacian. When the potential function vanishes at infinity, we obtain the existence of a ground state\nsolution for the fractional Choquard equation by using a non-Nehari manifold method. Moreover,\nin the zero mass case, we obtain a nontrivial solution by using a perturbation method. The results\nimprove upon those in Alves, Figueiredo, and Yang (2015) and Shen, Gao, and Yang (2016)....
In this paper, we present several new inequalities for weaving frames in Hilbert spaces\nfrom the point of view of operator theory, which are related to a linear bounded operator induced by\nthree Bessel sequences and a scalar in the set of real numbers. It is indicated that our results are more\ngeneral and cover the corresponding results recently obtained by Li and Leng. We also give a triangle\ninequality for weaving frames in Hilbert spaces, which is structurally different from previous ones....
As a nontrivial application of the abstract theorem developed in our recent paper titled\nâ??Limit-periodic solutions of difference and differential systems without global Lipschitzianity\nrestricitionsâ?, the existence of limit-periodic solutions of the difference equation from the title is\nproved, both in the scalar as well as vector cases. The nonlinearity h is not necessarily globally\nLipschitzian. Several simple illustrative examples are supplied....
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