Common fixed point theorems for four mappings on cone b-metric spaces over Banach algebras

Abstract

The purpose of this paper is to obtain several common fixed point theorems for four mappings in the setting of cone b-metric spaces over Banach algebras. The obtained results generalize, complement, and improve some results in the literature. Moreover, we give some supportive examples for our conclusions. In addition, an application in the solution of a class of equations is given to illustrate the superiority of the main results.

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

“…We begin with the definitions of known notions as well as known results from cone metric and cone b-metric spaces (for more details see [17][18][19][20][21][22][23][24][25][26][27][28][29][30][31][32]) over Banach algebra, respectively. Definition 1.…”

“…Next, to assure the uniqueness of fixed points in above theorems, we use the following property (see [26,27] Please note that Theorem 3, due to symmetry, improves and generalizes Theorem 2.1 in [18] and Theorem 3.3 in [5]. Theorem 5 ([18]).…”

“…The cone b-metric space over a BA with constant s ≥ 1 was introduced in [18] as a generalization of a b-metric space. Mitrović and Hussain [19] initiated the notion of cone b-metric space over a BA with constant s e. Definition 2 ([19]).…”

Fixed Point Results under Generalized c-Distance in Cone b-Metric Spaces Over Banach Algebras

“…The results of Liu and Xu are significant, in the sense that cone metric spaces over a Banach algebra are not equivalent to metric spaces. Hence, some interesting results about fixed point theory in cone metric spaces over a Banach algebra and in cone b-metric spaces over a Banach algebra with its applications were proved in [4][5][6].…”

“…Obviously, for s = 1, a cone b-metric space over a Banach algebra A is a cone metric space over same Banach algebra A. In addition, for definitions such as convergent and Cauchy sequences, c-sequence, completeness, continuity, and examples in cone b-metric spaces over Banach algebra A, we refer to [5,6]. In the sequel, let P be a solid cone and (X, d) be a cone b-metric space over a Banach algebra A with coefficient s ≥ 1.…”