Darbo's fixed point theorem and its generalizations play a crucial role in the existence of solutions in integral equations. Meir-Keeler condensing operators is a generalization of Darbo's fixed point theorem and most of other generalizations are a special case of this result. In recent years, some authors applied these generalizations to solve several special integral equations and some of the...

In this article, we use two concepts, measure of non-compactness and Meir-Keeler condensing operators. The measure of non-compactness has been applied for existence of solution nonlinear integral equations, ordinary differential equations and system of differential equations in the case of finite and infinite dimensions by some authors. Also Meir-Keeler condensing operators are shown in some pa...

Motivated by the open question posed H. K. XU in [39] (Question 2:8), Belhadj, Ben Amar and Boumaiza introduced [5] concept of Meir-Keeler condensing operator for self-mappings a Banach space via an arbitrary measure weak noncompactness. In this paper, we introduce Meir- Keeler nonself-mappings noncompactness establish fixed point results under condition Leray-Schauder type. Some basic hybrid t...

In this article to prove existence of solution of infinite system of nonlinear integral equations, we consider the space of solution containing all convergence sequences with a finite limit, as with a suitable norm is a Banach space. By creating a generalization of Meir-Keeler condensing operators which is named as F-generalized Meir-Keeler condensing operators and measure of noncompactness, we...

In this paper, we generalize the Meir-Keeler condensing  operators  via a concept of the class of operators  $ O (f;.)$, that was given by Altun and Turkoglu [4], and apply this extension to obtain some tripled fixed point theorems.  As an application of this extension, we  analyze the existence of solution for a system of nonlinear functional integral equations of Volterra type. Finally,  we p...

Our aim in this paper is to study the existence of solution sets and its topological structure for non-localfractional differential equations on half-line a Banach space using Riemann-Liouville definition. Themain result based Meir-Keeler fixed point theorem condensing operators combined with measure ofnon-compactness. An example given illustrate feasibility our main result.

In this article, we establish certain sufficient conditions to show the existence of solutions a fractional differential equation with ?-Riemann-Liouville and ?-Caputo derivative in special Banach space. Our approach is based on fixed point theorems for Meir-Keeler condensing operators via measure non-compactness. Also an example given illustrate our approach.

The Meir-Keeler contraction, an important generalization of the classical Banach contraction has received enormous attention during the last four decades. In this paper, we present a review of Meir-Keeler type fixed point theorems and obtain some results using general Meir-Keeler type conditions for a sequence of maps in a metric space. Further, a recent result of Meir-Keeler type common fixed ...

Recommended by Sehie Park We prove that the recent fixed point theorem for contractions of integral type due to Branciari is a corollary of the famous Meir-Keeler fixed point theorem. We also prove that Meir-Keeler contractions of integral type are still Meir-Keeler contractions.

‎In this article‎, ‎we discuss about solvability of infinite systems of singular integral equations with two variables in the Banach sequence space $C(I times I‎, ‎c)$ by applying measure of noncompactness‎ and Meir-Keeler condensing operators‎. By presenting an example, we have illustrated our results‎. ‎For validity of the results we introduce a modified semi-analytic method in the case of tw...