Fixed Point Theorems for a Class ofα-Admissible Contractions and Applications to Boundary Value Problem

Abstract

A class ofα-admissible contractions defined via altering distance functions is introduced. The existence and uniqueness conditions for fixed points of such maps on complete metric spaces are investigated and related fixed point theorems are presented. The results are reconsidered in the context of partially ordered metric spaces and applied to boundary value problems for differential equations with periodic boundary conditions.

A fixed point theorem for generalized contractive type set-valued mappings with application to nonlinear fractional differential inclusions

“…Proof. Let T be defined as (9). It is easy to check, fixed points of T are solutions of problem (8).…”

Fixed point results for generalized contractive mappings involving altering distance functions on complete quasi-metric spaces and applications

“…Furthermore, Alsulami et al [4] gave the definition of a class of α-admissible contraction via altering distance function. The results were reconsidered in the context of partially ordered metric spaces and applied to boundary value problems for differential equations with periodic boundary conditions.…”

“…The proof is trivial, here we omit the detail. The readers are referred to the proof of Theorem 20 in [4]. Theorem 4.5.…”

An Ulam stability result on quasi-b-metric-like spaces

“…For recent results related with˛-admissible mappings, see [18,19]. In their work Samet et.al [5], studied˛ -contractive mappings and their fixed points.…”