Coupled Fixed-Point Theorems in Theta-Cone-Metric Spaces

This paper gives further generalizations of some well-known coupled fixed-point theorems. Specifically, Theorem 3 of the paper is the generalization of the Baskar–Lackshmikantham coupled fixed-point theorem, and Theorem 5 is the generalization of the Sahar Mohamed Ali Abou Bakr fixed-point theorem, where the underlying space is complete θ -cone-metric space.

Solving a Class of Integral Equations via Contractive Mapping with Rational Type

In this paper, using rational type contractive conditions, the existence and uniqueness of common coupled fixed point theorem in the set up of Gb-metric spaces is studied. The derived result cover and generalize some well-known comparable results in the existing literature. Then we use the derived results to prove the existence and uniqueness solution for some classes of integral equations. Further more, an example of such type of integral equation is presented.

Types of Fixed Points of Set-Valued Contraction Mappings for Comparable Elements

This paper is concerned with the study of the fixed points of set-valued contractions on ordered metric spaces. The first part of the paper deals with the existence of fixed points for these mappings where the contraction condition is assumed for comparable variables. A coupled fixed point theorem is also established in the second part.

A New Coupled Fixed Point Result in Extended Metric Spaces with an Application to Study the Stability of Set-Valued Functional Equations

In this paper, we introduce a new coupled fixed point theorem in a generalized metric space and utilize the same to study the stability for a system of set-valued functional equations.