Role of α-Pseudo-Univex Functions in Vector Variational-Like Inequality Problems
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In this paper, we introduce a new class of generalized convex function, namely, α-pseudo-univex function, by combining the concepts of pseudo-univex and α-invex functions. Further, we establish some relationships between vector variational-like inequality problems and vector optimization problems under the assumptions of α-pseudo-univex functions. Results obtained in this paper present a refinement and improvement of previously known results.
Keywordsα-pseudo-univex functions vector optimization vector variational-like inequality problems
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- 2.G. Mastroeni, Some remarks on the role of generalized convexity in the theory of variational inequalities, in Generalized Convexity and Optimization for Economic and Financial Decisions (ed. by G. Giorgi and F. Rossi), Pitagora Editrice, Bologna, Italy, 1999, 271–281.Google Scholar
- 3.F. Gianessi, Theorems of alternative, quadratic programs and complementarity problems, in Variational Inequality and Complementarity Problems (ed. by R. W. Cottle, F. Giannessi, and J. L. Lions), John Wiley and Sons, New York, 1980, 151–186.Google Scholar
- 4.F. Giannessi, Vector variational inequalities and vector equilibria: Mathematical Theories, Nonconvex Optimization and its Applications, 2000, 38: 423–432.Google Scholar
- 9.C. R. Bector, S. Chandra, S. Gupta, and S. K. Suneja, Univex sets, functions and univex nonlinear programming, in Lecture Notes in Economics and Mathematical Systems 405, Springer Verlag, Berlin, 1994, 1–18.Google Scholar
- 11.S. K. Mishra and G. Giorgi, Optimality and duality with generalized semi-univexity, Opsearch, 2000, 37: 340–350.Google Scholar
- 14.M. A. Noor, On generalized preinvex functions and monotonicities, Journal of Inequalities in Pure and Applied Mathematics, 2004, 5(4): Article 110.Google Scholar