In this paper, by using a new concept of strong convexity, we obtain sufficient conditions for Holder continuity of the solution mapping for a parametric weak vector equilibrium problem in the case where the solution mapping is a general set-valued one. Without strong monotonicity assumptions, the Holder continuity for solution maps to parametric weak vector optimization problems is discussed.

‎In this paper‎, ‎we study the Hölder continuity of solution mapping to a parametric variational inequality‎. ‎At first‎, ‎recalling a real-valued gap function of the problem‎, ‎we discuss the Lipschitz continuity of the gap function‎. ‎Then under the strong monotonicity‎, ‎we establish the Hölder continuity of the single-valued solution mapping for the problem‎. ‎Finally‎, ‎we apply these resu...

where Q <= Rm is a bounded domain, JS?W denotes m-dimensional Lebesgue measure, (p = (<p\..., (p) is a continuous transformation from Q to Rn (m ^ n) belonging to some Sobolev space W x p' (Q), and (px is the (almost everywhere defined) matrix function (d^/oxj). Here ƒ is a realvalued function o n Q x i ? n x M „ x m , where Mnxm is the space o f n x m matrices. Such integrals arise in the anal...