Common Fixed Point Theorem for Compatible Mappings in Fuzzy Cone Metric Spaces Using Altering Distance Function

In this paper, we establish new common fixed point theorems for compatible mappings in fuzzy cone metric spaces by employing altering distance functions. Our results extend, generalize, and unify several existing fixed point theorems in fuzzy metric spaces, cone metric spaces, and probabilistic metric spaces. The approach using altering distance functions provides flexibility in handling convergence under vagueness and partial ordering induced by cones. An illustrative example demonstrates the validity of our main result, and possible applications to nonlinear functional analysis and differential equations are discussed.

Common Fixed Point, Compatible Mappings, Fuzzy Cone Metric Spaces, Weekly Compatible Mappings, Altering Distance Functions

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