Multivalued Contractive-Type Extensions with Stability and Well-Posedness in Cone b-Metric Spaces under (λ, s)-Convexity and Applications

Abstract

We introduce new extensions of multivalued contractive fixed point results in complete cone b-metric spaces endowed with a normal cone structure. By developing a λ-iterative scheme combined with an approximate Hausdorff selection technique, we establish original Nadler-type and Berinde-type results with explicit convergence estimates depending on the b-metric coefficient s and the iteration parameter λ.
In addition, we prove a Berinde-type fixed point theorem for weak multivalued contractions, together with stability and well-posedness results under the sharp condition sδ < 1. The stability theorem provides quantitative bounds for perturbations of contractive multivalued operators, while the well-posedness result guarantees convergence of approximate solutions to the unique fixed point.
Applications to vector optimization and Nash-type equilibrium problems are presented within the framework of (λ, s)-convexity. The results extend classical fixed point theorems of Nadler and Berinde to the ordered and relaxed triangle inequality setting of cone b-metric spaces.