Fixed Point Theorems in Complete Cone Metric Spaces over Banach Algebras

Abstract

The notion of C-class functions in Banach algebras is introduced. By using such concept, a new fixed point theorem is established. An example to illustrate main theorem is given. Finally, applications of our main result to cyclic mappings and weak contraction type mappings are given.

Common fixed point theorems on quasi-cone metric space over a divisible Banach algebra

“…Author details 1 Department of Mathematics and Computer Sciences, Transilvania University of Brasov, Brasov, Romania. 2 Department of Mathematics, Basic Science Faculty, University of Bonab, Bonab, Iran. 3 Department of Mathematics, Farhangian University, Qazvin, Iran.…”

“…This notion became popular and raised interest among researchers after the paper of Huang and X. Zhang [1] in 2007. Since then, a number of authors got the characterization of several known fixed point theorems in the context of Banach-valued metric space, such as, [2][3][4][5][6][7][8][9][10][11][12][13][14][15][16][17][18][19][20].…”

Fredholm integral equation in composed-cone metric spaces

“…They proved some fixed point theorems of contractive mappings on cone metric spaces. Despite all of these studies on cone metric spaces [15][16][17][18][19][20], and Meng and Cho studying algebraic cone metric spaces [21,22], there is much work concerning b-cone metric spaces, for instance, [23][24][25] Hence, by utilizing the concepts in [9,10], this study presents a generalization that represents type I composed cone metric spaces and type II composed cone metric spaces. The examples are for type I composed cone metric space, not cone metric space, and type II composed cone metric space, not for type I composed cone metric space.…”

Fixed Point Results in Complete Random Cone Metric Spaces Over Banach Algebra

“…31-37, 2023 point outcomes were constructed by Smriti Mehta et al [3]. By utilising complete cone metric spaces, Seong-Hoon Cho [4] established the idea of C-class functions and cyclic (α, β) -admissible mappings in Banach algebras. Also some important paper for references here [5,6,7,8,9,10,11,12].…”

“…In this paper, we use reference article [4,13] for Random cone metric spaces (RCMS) instead of cone metric spaces. In this work unique fixed point is referred to as "UFP" and fixed point is referred to as "FP".…”