Some properties of sets, functions, and multi-objective optimization problems using p-convexity

In this paper, we investigate the concept of p-convexity for sets and functions in n-dimensional Euclidean space. We establish novel algebraic and topological results within this generalized convexity framework. Furthermore, we analyze multi-objective optimization problems, with a particular emphasis on weakly efficient minima, under the assumption of $p$-convexity of the component functions. Several characterizations and properties of the corresponding solution sets are derived.