Common fixed point theorems for a class of (s, q)-contractive mappings in b-metric-like spaces and applications to integral equations

Abstract

In this paper, we establish fixed point theorems for one and two selfmaps in b-metric-like spaces, using (s, q)-contractive and F-(ψ, φ, s, q)-contractive conditions, defined by means of altering distances and 𝓒-class functions. Our theorems unify, extend and generalize corresponding results in the literature.

A Solution of Fredholm Integral Equation by Using the Cyclic η s q -Rational Contractive Mappings Technique in b-Metric-Like Spaces

“…Continuing in this direction, this paper discusses some common fixed point theorems for cyclic η q s -rational contractive mappings in b-metric-like spaces. The obtained results here unify, improve the results of [24,28] and generalize various comparable known results. After that, we discuss some fixed point theorem in the framework of b-metric-like spaces endowed with a graph.…”

“…It is noted that the class of η q s -rational contraction mapping is a strictly larger class than (s, q)-Dass and Gupta contraction and hence a larger class than Dass and Gupta and Jaggi contraction [28].…”

Fixed-Point Results for a Generalized Almost (s, q)—Jaggi F-Contraction-Type on b—Metric-Like Spaces

“…The paper generalizes known contraction conditions and the obtained fixed point results, generalized several results known before such as Banach contraction [1], Jaggi-contraction [28], [29], and Ciric almost contraction [30]. Furthermore, as it has been observed in studies, fixed point results in b−metric-like spaces can be derived from the results of ordinary and b−metric spaces under some suitable conditions.…”

Some new results on (s,q)-Dass-Gupta-Jaggi type contractive mappings in b-metric-like spaces

“…If we take X = A i , i = 1, 2, ..., l, in the above case, then the mapping f reduces to η q s −rational contraction mapping of Dass-Gupta-Jaggi type (see [10], [13], [16], [21], [51]).…”