Weakly compatible and quasi-contraction results in fuzzy cone metric spaces with application to the Urysohn type integral equations

Advances in Difference Equations

article

Jabeen, Shamoona¹  Ur Rehman, Saif²  Zheng, Zhiming¹  Wei, Wei¹ 

[1] School of Mathematical Sciences, Beihang University;Department of Mathematics, Gomal University

关键词: Coincidence point;    Common fixed point;    Fuzzy cone metric space;    Weakly compatible mappings;    Contraction conditions;   

DOI  :  10.1186/s13662-020-02743-5

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

In this paper, we present some weakly compatible and quasi-contraction results for self-mappings in fuzzy cone metric spaces and prove some coincidence point and common fixed point theorems in the said space. Moreover, we use two Urysohn type integral equations to get the existence theorem for common solution to support our results. The two Urysohn type integral equations are as follows: $$\begin{aligned} &x(l)= \int _{0}^{1}K_{1}\bigl(l,v,x(v) \bigr)\,dv+g(l), \\ &y(l)= \int _{0}^{1}K_{2}\bigl(l,v,y(v) \bigr)\,dv+g(l), \end{aligned}$$ where $l\in [0,1]$ and $x,y,g\in \mathbf{E}$, where E is a real Banach space and $K_{1},K_{2}:[0,1]\times [0,1]\times \mathbb{R}\to \mathbb{R}$.

【 授权许可】

CC BY