Coupled fixed point theorems for contractive mappings involving new function classes and applications

Abstract

The aim of this paper is to introduce the notions of α-(F , H)-ϕ, ψ and µ-(F , H)-ϕ, ψ contractions and present several coupled fixed point theorems for this type of contractions in the set of ordered metric spaces. Several examples are offered to illustrate the validity of the obtained results. As an application, the existence of a solution of Fredholm nonlinear integral equations are also investigated.

Common fixed point results of generalized almost rational contraction mappings with an application

“…Due to its applications in mathematics and other related disciplines, Banach contraction principle has been generalized in many directions. Extensions of Banach contraction principle have been obtained either by generalizing the domain of the mapping or by extending the contractive condition on the mappings (see, [1,2,3,4,5,6,7,10,11,13,14,15,16,18,19,22,23,24,26,27,28,29,30,31,32,34,35] and references therein).…”

“…Following this trend, Samet et al [34] first introduced α-admissible mappings and then α-ψ-contractive type mappings to obtain some interesting generalizations of Banach contraction principle. For more results in this direction, we refer to [6,13,14,16,17,20,21,22,24,28,30,32] and references mentioned therein. Recently, Alizadeh et al [5] defined the concept of cyclic (α, β)-admissible mapping as follows: Definition 1.1 ( [5]).…”

Simulative Suzuki-Gerghaty Type Contraction With $\mathscr{C}$ -Class Functions and Applications

“…Some examples of simulation functions and C G -simulation functions are: For more examples of simulation functions and C G -simulation functions see [2,12,15,16,19,22]. We denote by F the class of all functions β : [0, ∞) → [0, 1) satisfying β(t n ) → 1, implies t n → 0 as n → ∞.…”

An Investigation of the Common Solutions for Coupled Systems of Functional Equations Arising in Dynamic Programming

“…Banach fixed-point theorem [1], considered to be the source of metrical fixed-point theory, has been generalized by many researchers; see [2][3][4][5]. One of the most interesting generalizations of this theorem was given by Jleli and Samet [6] by introducing the notion of ϑ-contraction.…”