It is well known that the classical contraction mapping principle of Banach is a fundamental result in fixed point theory. Several authors have obtained various extensions and generalizations of Banach’s theorems by considering contractive mappings on different metric spaces. Huang and Zhang [1] have replaced real numbers by ordering Banach space and have defined a cone metric space. They have ...

Abstract In this work, we consider a generalized quantum fractional Sturm–Liouville–Langevin difference problem with terminal boundary conditions. The relevant results rely on Mönch’s fixed point theorem along theoretical method by terms of Kuratowski measure noncompactness (MNC) and the Banach contraction principle (BCP). Furthermore, two dynamical notions Ulam–Hyers (UH) (GUH) stability are a...

This article is concerned with the study of a new class hybrid fractional q-integro-difference equations involving Caputo type q-derivatives and Riemann-Liouville q-integrals different orders nonlocal q-integro-initial condition. An existence result for given problem obtained by means Krasnoselskii’s fixed point theorem, whereas uniqueness its solutions shown applying Banach contraction mapping...

The prime aim of the present paper is to continue developing theory tempered fractional integrals and derivatives a function with respect another function. This combines calculus $\Psi$-fractional calculus, both which have found applications in topics including continuous time random walks. After studying basic $\Psi$-tempered operators, we prove mean value theorems Taylor's for Riemann--Liouvi...

for all x, y ∈ X. Kannan [] proved that if X is complete, then a Kannan mapping has a fixed point. It is interesting that Kannan’s theorem is independent of the Banach contraction principle []. Also, Kannan’s fixed point theorem is very important because Subrahmanyam [] proved that Kannan’s theorem characterizes the metric completeness. That is, a metric space X is complete if and only if ev...

The notion of partial metric space [1], represented by the abbreviation PMS, departs from the usual metric spaces due to removing the assumption of self-distance. In other words, in PMS self-distance needs not to be zero. This interesting distance function is defined by Matthews [1], as a generalization metric to study in computer science, in particular, to get a more efficient programs in comp...

We solve a question posed by E. Karapinar, F. Khojasteh and Z.D. Mitrović in their paper “A Proposal for Revisiting Banach Caristi Type Theorems b-Metric Spaces”. also characterize the completeness of b-metric spaces with help variant contractivity condition introduced authors aforementioned article.

Abstract This paper is devoted to study the existence and uniqueness of solutions a one parameter family nonlinear Riemann–Liouville fractional differential equations with mixed boundary value conditions. An exhaustive sign related Green’s function carried out. Under suitable assumptions on asymptotic behavior part equation at zero infinity, by application fixed point theory compact operators d...