In this paper, we introduce generalized cyclic φ-contraction maps in metric spaces and give some results of best proximity points of such mappings in the setting of a uniformly convex Banach space. Moreover, we obtain convergence and existence results of proximity points of the mappings on reflexive Banach spaces

Banach contraction principle is a fundamental result in fixed point theory and has been applied and extended in many different directions. In 2002, Branciari [3] obtained a fixed point theorem for a single mapping satisfying an analogue of Banach’s contraction principle for an integral type inequality. Aliouche [2] established a common fixed point theorem for weakly compatible mappings in symme...

This paper is devoted to the study of stochastic fractional differential equations. Particularly, we existence and uniqueness solutions nonlinear weighted impulsive ψ -Hilfer neutral integro-fractional system with infinite delay. We obtain results help fixed-point theorems Banach contraction principle. Additionally, inve...

The main object of this paper is to investigate the existence solutions for a self-adjoint coupled system nonlinear second-order ordinary differential equations equipped with nonlocal multi-point boundary conditions on an arbitrary domain. We apply Leray–Schauder alternative, Schauder fixed point theorem and Banach contraction mapping principle in order derive results, which are then well-illus...

The paper focuses on exploring the existence and uniqueness of a specific solution to class Caputo impulsive fractional differential equations with boundary value conditions Banach space, referred as (ω,ρ)-BVP solution. proof main results this study involves application contraction mapping principle Schaefer’s fixed point theorem. Furthermore, we provide necessary for convexity set solutions an...

The well known contraction mapping principle or Banach’s fixed point theorem asserts: The method for successive substitutions converges only linearly to a fixed point of an operator equation in a Banach space setting [5], [7]. In practice, if Newton’s method is used one ignores the additional information about the contraction mapping information. Werner in [9] provided a local analysis for a Ne...