Fixed Point Theorems for Multivalued Weak Contractions in Cone Metric Spaces

TL;DR

This paper extends fixed point theorems for multivalued weak contractions within cone metric spaces, providing new existence, uniqueness, and convergence results with applications to differential inclusions.

Contribution

It generalizes Berinde's weak contraction principles to multivalued mappings in cone metric spaces, including iterative schemes and stability analysis.

Findings

Established generalized fixed point theorems for multivalued weak contractions.

Developed iterative approximation schemes with explicit convergence rates.

Demonstrated applications to differential inclusions and variational inequalities.

Abstract

This article presents a deep investigation of fixed points for multivalued weak contractions in cone metric spaces. We extend Berinde weak contraction principles to the multivalued setting in cone metric spaces, developing existence, uniqueness, and convergence results. Using the structure of normal cones in Banach spaces, we prove generalized fixed-point theorems for set-valued mappings satisfying weak contractive conditions. The theoretical framework includes iterative approximation schemes with explicit convergence rates and stability analysis of fixed point sets. In the end, some applications to differential inclusions and variational inequalities demonstrate the utility of our results in nonlinear analysis.