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

Abstract

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 condensing operators and using them we propose new fixed point results. Our results generalize and extend some comparable results from the literature. Additionally, as an application, we apply the obtained fixed point theorems to study the nonlinear functional integral equations.

Best proximity point (pair) results via MNC in Busemann convex metric spaces

“…Results for β-ψ-condensing operator. Now we recall the concept of β-admissibility which is introduced by Rehman et al in [19], with a slight modification as follows.…”

The Inertial Sub-Gradient Extra-Gradient Method for a Class of Pseudo-Monotone Equilibrium Problems

“…As long as we know, Mu and Oettli [6] established this particular notion "equilibrium problem" in 1992 and was advanced further by Blum and Oettli [1]. Several authors have achieved and generalized many results with regard to the existence of an equilibrium problem solution (e.g., see [7][8][9][10][11] and the references therein). The development of new iterative methods and the examination of their converging analysis are among the most effective and valuable research directions in equilibrium theory.…”

A Self-Adaptive Extra-Gradient Methods for a Family of Pseudomonotone Equilibrium Programming with Application in Different Classes of Variational Inequality Problems

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