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Coupled fixed point theorems under new coupled implicit relation in Hilbert spaces

Kim Kyung Soo

Demonstratio Mathematica

2022

Vol. 55, nr 1

81--89

The aim of this paper is to study existence and uniqueness of coupled fixed point for a family of self-mappings satisfying a new coupled implicit relation in a Hilbert space. We also prove well-posedness of a coupled fixed point problem.

Coupled fixed point theorems in partially ordered metric spaces

Rao N. Seshagiri, Kalyani K.

Fasciculi Mathematici

2020

nr 64

77--89

This paper deals with some coupled fixed point theorems for a mapping with mixed monotone property and satisfying certain generalized rational contraction in a partially ordered metric space. Also, the result for the existence and uniqueness of a coupled fixed point to the map is given under ordered relation in a space. These results generalize and extend some existing results in the literature.

Generalizations of Darbo’s fixed point theorem for new condensing operators with application to a functional integral equation

Rehman Habib ur, Gopal Dhananjay, Kumam Poom

Demonstratio Mathematica

2019

Vol. 52, nr 1

166--182

In this paper, we provide some generalizations of the Darbo’s fixed point theorem associated with the measure of noncompactness and present some results on the existence of the coupled fixed point theorems for a special class of operators in a Banach space. To acquire this result, we define α-ψ and β-ψ con-densing operators and using them we propose new fixed point results. Our results generalize and extendsome comparable results from the literature. Additionally, as an application, we apply the obtained fixedpoint theorems to study the nonlinear functional integral equations.

Some common coupled fixed point theorems in Sb - metric spaces

Khomdram B., Rohen Y.

Fasciculi Mathematici

2018

Nr 60

79--92

In this paper, we prove some common coupled fixed point theorems for mapping satisfying a nonlinear contraction in Sb-metric space and some results are also given in the form of corollary. Also, some examples are given to verify the main results.