Some fixed point results on \(\mathcal{N}_{b}\) -cone metric spaces over Banach algebra

[摘要] 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.

[学科分类] 航空航天科学

[关键词] \(\mathcal{N}_{b}\) -cone metric spaces over Banach algebra;c -sequence;Iterative algorithm;Coupled fixed points