Some fixed point theorems in b-metric-like spaces

Abstract

In this work, some fixed point and common fixed point theorems are investigated in b-metric-like spaces. Some of our results generalize related results in the literature. Also, some examples and an application to integral equation are given to support our main results. MSC: 47H10; 54H25

Fixed point theorems for generalized F-contractions in b-metric-like spaces

“…We say that T is continuous on X if T is continuous at all x ∈ X. Remark 1.7 ( [9]). Let (X, σ) be a b-metric-like space and let f : X → X be a continuous mapping.…”

“…Recently, the notion of b-metric-like spaces were introduced by Alghamdi [4] and some fixed point theorems were studied in such spaces [4,9].…”

Application of Fixed Point Results on Rational F-Contraction Mappings to Solve Boundary Value Problems

“…Many papers related to fixed point results in b-metric-like spaces appear in literature, some of them are [3,7,[10][11][12][13] and references therein.…”

Discussion on a coupled fixed point theorem for single-valued operators in b-metric spaces

“…Let X be a set and let s 1 be a given real number. A functional d : X × X −→ R + is said to be a b-metric if the following conditions are satisfied: Since then, several authors have established the existence and uniqueness theorems of fixed points for single-valued operators in b-metric spaces [2,3,6,11,13,15].…”