Abstract

This paper focuses on the stability analysis of Minty and Stampacchia vector equilibrium problems, particularly in scenarios where both the feasible set and the objective map are subject to perturbations. The research utilizes advanced mathematical tools such as cone-semicontinuity and generalized level closedness properties of objective maps to derive significant upper stability results for these vector equilibrium problems. Additionally, the study explores lower stability outcomes by applying generalized cone-convexity assumptions on objective maps, notably without the need for traditional monotonicity properties, which are often restrictive in practical applications.

The findings in this paper represent a substantial contribution to the field of vector equilibrium problems by broadening the scope of existing stability theories. This work overcomes some of the limitations of prior research, which typically required strict continuity of objective maps or the solvability of auxiliary problems. By relaxing these conditions, the paper offers a more robust framework for analyzing the stability of vector equilibrium problems, making the results applicable to a wider array of practical situations, including those in physics, engineering, economics, and social network analysis.

Ultimately, this paper advances the understanding of stability in vector equilibrium problems, providing a foundation for future research and potential applications in various scientific and engineering disciplines. The theoretical developments presented here not only enhance the mathematical modeling of complex systems but also contribute to the practical implementation of these models in real-world scenarios. Furthermore, several illustrative examples are provided to demonstrate the applicability and effectiveness of the obtained stability results. These examples highlight the flexibility of the proposed approach and emphasize its potential usefulness in addressing complex equilibrium models arising in optimization, decision science, and multi-criteria analysis.