Solution Sensitivity of a Class of Variational Inequalities

Abstract

We obtain a result on the Holder continuity of solutions to variational inequalities of the type previously studied by Noor, Mukherjee, and Verma. ᮊ 1997 Academic Press

Sensitivity analysis for abstract equilibrium problems

“…The result of this paper unifies and improves many previous results (on the continuity of solutions to variational inequalities) in the literature [3][4][5][6][7][8][9]11,12,[14][15][16][17][18][20][21][22], where no appeal is made to geometrical properties of the space. Even though we have worked under arbitrary constraints K λ with Hölder-property that have been decisive in our treatmentwe have obtained, in similar spirit of Domokos [4], the best lower bound for the continuity modulus despite of the properties of the boundary of K λ .…”

On the Hölder continuity of solutions to parametric multivalued vector equilibrium problems

“…As an example of applications we derive a result for variational inequality problems. For Lipschitz and Hölder continuity of solutions of variational inequality problems and other related problems the reader is referred to [5,7,8,10,11], while for Lipschitz continuity of solutions of quasivariational inclusions, to [1,6].…”

Smooth dependence on parameters of solutions and contact regions for an obstacle problem

“…Various methods were developed for the study of continuation for variational inequalities (see, e.g., [1,[6][7][8][9][10]12]). However, as far as we know, no result about a smoothness (differentiability) of continuation or bifurcation branches has been published with the exception of the papers mentioned above.…”