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

Abstract

In this article, we prove some fixed-point theorems in b-dislocated metric space. Thereafter, we propose a simple and efficient solution for a non-linear integral equation and non-linear fractional differential equations of Caputo type by using the technique of fixed point.

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

“…Note that H −1 is a Banach contraction in the setting of an B e -metric space. In addition, since 1 κ < 1, we can conclude that H −1 has a unique fixed point by using Theorem 3 of Kamran et al [13]. This completes the proof of the theorem.…”

“…There is an effort, however, to convert fixed point theorems that are in the theory of topological fixed point theory into non-linear integral equations and differential equations. This effort is spearheaded major developments in related research areas ( see for more info References [6][7][8][9][10][11][12][13]).…”

Multivalued Fixed Point Results in Dislocated b-Metric Spaces with Application to the System of Nonlinear Integral Equations

“…Due to its significance, a large number of authors have proved many interesting multiplications of his result (see ). Recently, Kumari et al [22] discussed some fixed point theorem in b-dislocated metric space and proved efficient soloution for a non-linear integral equations and non-linear fractional differential equations. In this paper, we have obtained common fixed point for a pair of multivalued mappings satisfying generalized rational type F-dominated contractive conditions on a closed ball in complete dislocated b-metric space.…”

Fixed Point Results for the Family of Multivalued F-Contractive Mappings on Closed Ball in Complete Dislocated b-Metric Spaces

“…An example which supports the proved results is also given. Moreover, we investigate our results in a better framework of dislocated b-metric space (see [28][29][30]). New results in ordered spaces, partial b-metric space, dislocated metric space, partial metric space, b-metric space, and metric space can be obtained as corollaries of our results.…”