Some α − ϕ -Fuzzy Cone Contraction Results with Integral Type Application

Abstract

In this paper, we define $\alpha$ -admissible and $\alpha$ - $\varphi$ -fuzzy cone contraction in fuzzy cone metric space to prove some fixed point theorems. Some related sequences with contraction mappings have been discussed. Ultimately, our theoretical results have been utilized to show the existence of the solution to a nonlinear integral equation. This application is also illustrative of how fuzzy metric spaces can be used in other integral type operators.