Common Fixed Point Theorems on Generalized Ratio Contraction Mapping in Extended Rectangular b-Metric Spaces

Abstract

In this paper, we propose and prove the common fixed point theorems on generalized contraction mappings in extended rectangular b-metric spaces by utilizing the weakly compatible function property. PreliminariesIn the following section, we need some definitions to govern our theorems.Definition 1 (see [1]). Let X be a nonempty set. A mappingfor all x, y, s ∈ X. e pair (X, d b ) is called a b-metric space.Definition 2 (see [4]). Let X be a nonempty set. A mappingsatisfies the following conditions:for all x, y, s ∈ X. e pair (X, d b ) is called an extended b-metric space.Definition 3 (see [6]). Let X be a nonempty set. A mapping d b : X × X ⟶ [0, ∞) is called rectangular b-metric, if there exists b ≥ 1 such that d b satisfies the following conditions:(1) d b (x, y) � 0, if and only if x � y

Existence and Uniqueness of Fixed Point for Cyclic Mappings in Quasi-αb-Metric Spaces

“…Definition 2.1. [19], [20] Let ℜ be define a non-empty set for 𝑘 ∈ [1, ∞). Let 𝑑 𝑐 ∶ ℜ × ℜ → [0, ∞) defined as mapping and for all 𝑟, 𝑠, 𝑡 ∈ ℜ, has to satisfy the conditions below:…”