Coupled fixed point theorems in C*-algebra-valued b-metric spaces

Abstract

In this paper, we give some coupled fixed point results in the framework of C * -algebra-valued b-metric spaces and in particular in the setting of C * algebra-valued metric spaces. These results, with shorter proofs, generalize and improve other theorems recently introduced. We have used a method of reducing coupled fixed point results to the respective ones for mappings with one variable in the framework of b-metric spaces. Finally, two examples are given to support our theoretical work.

On the C ∗ -algebra valued G-metric space related with fixed point theorems

“…To see that the fixed point is unique suppose that x = y such that T x = x, T y = y. Then by (1) (Following Zhenhu et all [10]), We get G (a, b, c) and so, T has a unique fixed point.…”

“…A. Zada et al [9] considered graph theory and studied on common fixed points in the C * -valued metric space endowed with the graph G under G-contractive condition. S. Radenovic and his collegues [10] used a method to reducing coupled fixed point results to the respective ones for mappings with one variable in the framework of b-metric spaces. They also demonstrated that each C * -algebra-valued b-metric space is a cone b-metric space over normal cone with normal constant equal to 1.…”

On Generalized Hardy–Rogers Type α-Admissible Mappings in Cone b-Metric Spaces over Banach Algebras

“…For more details on other results from C * -algebra-cone metric spaces that is, from C * -algebra-cone b-metric spaces the reader can be see [40][41][42]44].…”

Unification of common fixed point in C *-algebra valued metric spaces

“…Afterward, many researcher work on ‫ܥ‬ * -algebra valued metric space and proved different kind of results. (For reference see [2,3,6,16,17]). In the present manuscript, fixed point theorem are proved with the help of E.A.…”