Fixed Point Theorems for Kannan and Chatterjea-type Mappings in Probabilistic Cone Metric Spaces

Abstract: This paper establishes novel fixed point theorems for Kannan-type and Chatterjea-type mappings in probabilistic cone metric spaces. By integrating probabilistic distance functions with cone-valued structures, we generalize classical fixed point results to settings with inherent uncertainty. Our approach leverages the distributional properties of probabilistic metrics and the order structure of cones to develop contraction conditions ensuring the existence and uniqueness of fixed points. Applications include stochastic processes, random operators, and uncertainty modeling in functional equations. The results significantly extend the scope of fixed point theory in probabilistic analysis and its applications