A New Approach to the Solution of the Fredholm Integral Equation via a Fixed Point on Extended b-Metric Spaces

Abstract

It is very well known that real-life applications of fixed point theory are restricted with the transformation of the problem in the form of f ( x ) = x . (1) The Knaster–Tarski fixed point theorem underlies various approaches of checking the correctness of programs. (2) The Brouwer fixed point theorem is used to prove the existence of Nash equilibria in games. (3) Dlala et al. proposed a solution for magnetic field problems via the fixed point approach.

Some Fixed-Point Theorems in b-Dislocated Metric Space and Applications

“…More particularly, the techniques used to obtain fixed points in [1] have attracted several authors. In this scenario, many authors imposed various restrictions to obtain the existence of a fixed point (see for example [10][11][12][13][14][15]).…”

Solutions of the Nonlinear Integral Equation and Fractional Differential Equation Using the Technique of a Fixed Point with a Numerical Experiment in Extended b-Metric Space

“…For more interesting examples and basic results in δ e -metric space, we refer to [16][17][18][19][20]. For some recent modifications or developments to extended b−metric spaces, the reader may refer to the so-called controlled and double-controlled metric type spaces in [21,22] and for further fixed point investigations in extended b-metric spaces to [23].…”

A New Approach to the Solution of Non-Linear Integral Equations via Various FBe-Contractions

“…Observe that usually a b-metric is not a continuous functional. Analogously, the functional B e -metric is also not necessarily a continuous function [15][16][17][18][19].…”