Abstract
The main aim of this paper is to introduce the concept of mathcal{N}_{b}-cone metric spaces over a Banach algebra as a generalization of mathcal{N}-cone metric spaces over a Banach algebra and b-metric spaces. Also, we study some coupled common fixed point theorems for generalized Lipschitz mappings in this framework. Finally, we give an example and an application to the existence of solutions of integral equations to illustrate the effectiveness of our generalizations. Some results in the literature are special cases of our results.
Highlights
The concept of b-metric space has been introduced by Bakhtin [2] and Czerwik [4]
Their work contains some fixed point results for generalized Lipschitz mapping in cone metric spaces over Banach algebras
(2020) 2020:529 algebra presented by Fernandez et al [6], who generalized the concept of N -cone metric space and proved some fixed point results for generalized Lipschitz mapping in this new framework
Summary
The concept of b-metric space has been introduced by Bakhtin [2] and Czerwik [4]. Via this notion the Banach contraction principle has been extended in b-metric spaces by Czerwik. The study of N -cone metric spaces was started by Malviya and Fischer [15] They generalized the concept of D∗-metric spaces [1] to form a new space and defined asymptotically regular maps in N -cone metric spaces. Their work contains some fixed point results for generalized Lipschitz mapping in cone metric spaces over Banach algebras. Fernandez et al Advances in Difference Equations (2020) 2020:529 algebra presented by Fernandez et al [6], who generalized the concept of N -cone metric space and proved some fixed point results for generalized Lipschitz mapping in this new framework. Some coincidence point and common fixed point results for hybrid pairs of mappings on a cone b-metric space over a Banach algebra have been stated and proved by Malhotra et al [14]. 5. We investigate some coupled fixed point problems for generalized Lipschitz maps in Sect. The results of [26] are special cases of our results
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