Fixed point approach for solving a system of Volterra integral equations and Lebesgue integral concept in F$ _{\text{CM}} $-spaces

Abstract

The goal of this manuscript is to obtain some tripled fixed point results under a new contractive condition and triangular property in the context of fuzzy cone metric spaces (F$ _{\text{CM}} $-spaces). Moreover, two examples and corollaries are given to validate our work. Ultimately, as applications, the notion of Lebesgue integral is represented by the fuzzy method to discuss the existence of fixed points. Also, the existence and uniqueness solution for a system of Volterra integral equations are studied by the theoretical results.

Keywords

• tripled fixed point
• fuzzy cone metric spaces
• lebesgue-integrable mapping
• volterra integral equation