Common fixed point theorems of generalized Lipschitz mappings in cone b-metric spaces over Banach algebras and applications

Abstract

In this paper, we introduce the concept of cone b-metric space over Banach algebra and present some common fixed point theorems in such spaces. Moreover, we support our results by two examples. In addition, some applications in the solutions of several equations are given to illustrate the usability of the obtained results.

Fixed Point Results for Weakφ-Contractions in Cone Metric Spaces over Banach Algebras and Applications

“…Recently, Liu and Xu [14] introduced the concept of a cone metric space over Banach algebra, which is an interesting generalization of classic metric spaces. From then on, many authors focused on the investigation of fixed point in such spaces (see [15][16][17][18][19][20]). Stimulated and motivated by the previous work, throughout this paper, we introduce weak -contractions in the setting of cone metric spaces over Banach algebras and present some fixed point theorems for weak -contractions.…”

Quadruple random common fixed point results of generalized Lipschitz mappings in cone b-metric spaces over Banach algebras

“…In 2013, Liu and Xu [21] introduced cone metric space over Banach algebra by replacing Banach spaces with Banach algebra and proved some fixed point theorems of generalized Lipschitz mapping with weaker conditions on generalized Lipschitz constants. In 2015, Huang and Radenović [9] introduced the concept of cone b-metric space over Banach algebra and proved some common fixed point theorems of generalized Lipschitz mappings in such setting without assumption of normality. Random fixed point theorems are stochastic generalizations of classical fixed point theorems.…”

Some fixed point results for rational type and subrational type contractive mappings

“…Banach fixed point theorem [1] is one of the pivotal results in mathematical analysis. Many authors (see, e.g., [2]- [8]) not only extend this theorem but also consider fixed points in various abstract spaces.…”