Journal of Optimization Theory and Applications

, Volume 118, Issue 2, pp 327–338

Variational-Like Inequalities with Generalized Monotone Mappings in Banach Spaces

  • Y.P. Fang
  • N.J. Huang
Article

DOI: 10.1023/A:1025499305742

Cite this article as:
Fang, Y. & Huang, N. Journal of Optimization Theory and Applications (2003) 118: 327. doi:10.1023/A:1025499305742

Abstract

In this paper, we introduce two classes of variational-like inequalities with generalized monotone mappings in Banach spaces. Using the KKM technique, we obtain the existence of solutions for variational-like inequalities with relaxed η–α monotone mappings in reflexive Banach spaces. We present also the solvability of variational-like inequalities with relaxed η–α semimonotone mappings in arbitrary Banach spaces by means of the Kakutani-Fan-Glicksberg fixed-point theorem. The results presented in this paper extend and improve the corresponding results of Refs. 1–6.

Variational-like inequalitiesgeneralized monotone mappingsKKM mappingsη-hemicontinuityη-coercivity

Copyright information

© Plenum Publishing Corporation 2003

Authors and Affiliations

  • Y.P. Fang
    • 1
  • N.J. Huang
    • 1
  1. 1.Department of MathematicsSichuan UniversityChengdu, SichuanP. R. China