Dislocated quasi cone b-metric space over Banach algebra and contraction principles with application to functional equations

Abstract

In this paper we introduce dislocated and dislocated quasi version of a cone b-metric space over a Banach algebra as well as weak semi α-admissible and α-identical pair of mappings and prove common fixed point theorems for a pair of α-identical and weak α-admissible mappings in the aforesaid spaces. Our results are supported with suitable examples and an application to a system of m-tupled functional equations.

Fixed point theorem between cone metric space and quasi-cone metric space

“…-Example 2. 5 (see [25]). Assume 𝑋 = ℝ, 𝐸 = ℝ 2 , 𝑃 = {(𝑢, 𝑣) ∈ 𝐸: 𝑢, 𝑣 ≥ 0} and 𝑞: ℝ × ℝ ⟶ ℝ 2 is defined by (2),…”