Common Fixed-Point Theorems for Weakly Compatible Mapping in Neutrosophic Metric Space of Integral Type Using Common EA Property

Abstract

This manuscript focuses on developing and generalizing fixed-point results within the framework of neutrosophic metric spaces of integral type. By employing the common property (EA) and four self-mappings the study investigates the conditions necessary for the existence and uniqueness of fixed and common fixed points in neutrosophic metric spaces. To guarantee the validity of the results, the mappings under examination must meet certain contractive conditions and implicit relations such as being Lebesgue integrable and summable and non-negative. This work builds on the foundational concepts of fuzzy metric spaces and intuitionistic fuzzy metric spaces extending their applicability to the neutrosophic context. Nontrivial examples with graphical representations are given to demonstrate the theoretical conclusions and prove the proposed theorems' correctness and practical significance.  The manuscript also explores the relationships between various mappings and highlights the role of weak compatibility and continuity in achieving the common property (EA).