On New Extensions of Darbo’s Fixed Point Theorem with Applications

Abstract

In this paper, we extend Darbo’s fixed point theorem via weak JS-contractions in a Banach space. Our results generalize and extend several well-known comparable results in the literature. The technique of measure of non-compactness is the main tool in carrying out our proof. As an application, we study the existence of solutions for a system of integral equations. Finally, we present a concrete example to support the effectiveness of our results.

Solving a Nonlinear Fractional Integral Equation by Fixed Point Approaches Using Auxiliary Functions Under Measure of Noncompactness

“…Several academics have recently generalized Darbo's FPT, as seen in [15,21,26], by using various types of operator contraction. Through the use of weak JS-contractions in Banach spaces (BSs), Işik et al [27] have expanded Darbo's FPT. They have also derived the coupled FP theorem and used it to investigate the existence of solutions for a set of IEs.…”

Editorial Conclusion for the Special Issue “Fixed Point Theory and Computational Analysis with Applications”

“…Fixed point theory and applications (see [1][2][3][4][5][6][7][8][9][10][11][12][13][14][15][16]); • Computational analysis and applications (see [1,2,7,9,12,[15][16][17][18][19][20][21][22][23][24][25]).…”

Abstract Fixed-Point Theorems and Fixed-Point Iterative Schemes

“…Thus, the aim of this collection of papers is to cover some of the recent advancements in abstract research and in developing new useful applications. The specific topics mainly include both fixed-point theorems in generalized metric spaces and Banach spaces (see [1][2][3][4][5][6][7]) and fixed-point iterative schemes along with the convergence analysis of proposed solving algorithms (see [8][9][10][11][12][13][14]). In particular, we point the attention of the reader on the applications of fixed-point arguments to the context of various classes of differential equations (see [15][16][17][18]); for a similar approach to integral equations, see [19].…”