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

Advances in Difference Equations

article

Fernandez, Jerolina¹  Malviya, Neeraj²  Mitrović, Zoran D.³  Hussain, Azhar⁵  Parvaneh, Vahid⁶ 

[1] Department of Science, The Bhopal School of Social Sciences;Department of Mathematics, Government College;Nonlinear Analysis Research Group, Ton Duc Thang University;Faculty of Mathematics and Statistics, Ton Duc Thang University;Department of Mathematics, University of Sargodha;Department of Mathematics, Gilan-E-Gharb Branch, Islamic Azad University

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

DOI  :  10.1186/s13662-020-02991-5

学科分类：航空航天科学

来源: SpringerOpen

【 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.

【 授权许可】

CC BY