Abstract
We introduce some new classes of preinvex and invex functions, which are called
We introduce some new classes of preinvex and invex functions, which are called
M. A. Hanson, “On sufficiency of the Kuhn-Tucker conditions,” Journal of Mathematical Analysis and Applications, vol. 80, no. 2, pp. 545–550, 1981.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetS. R. Mohan and S. K. Neogy, “On invex sets and preinvex functions,” Journal of Mathematical Analysis and Applications, vol. 189, no. 3, pp. 901–908, 1995.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetM. A. Noor, “Nonconvex functions and variational inequalities,” Journal of Optimization Theory and Applications, vol. 87, no. 3, pp. 615–630, 1995.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetM. A. Noor, “On generalized preinvex functions and monotonicities,” JIPAM. Journal of Inequalities in Pure and Applied Mathematics, vol. 5, no. 4, pp. 1–9, 2004, article 110.
View at: Google Scholar | MathSciNetM. A. Noor, “Some new classes of nonconvex functions,” Nonlinear Functional Analysis and Its Applications, vol. 11, 2006.
View at: Google ScholarG. Ruiz-Garzón, R. Osuna-Gómez, and A. Rufián-Lizana, “Generalized invex monotonicity,” European Journal of Operational Research, vol. 144, no. 3, pp. 501–512, 2003.
View at: Google Scholar | Zentralblatt MATH | MathSciNetS. Schaible, “Generalized monotonicity—concepts and uses,” in Variational Inequalities and Network Equilibrium Problems (Erice, 1994), F. Giannessi and A. Maugeri, Eds., pp. 289–299, Plenum, New York, 1995.
View at: Google Scholar | Zentralblatt MATH | MathSciNetT. Weir and B. Mond, “Pre-invex functions in multiple objective optimization,” Journal of Mathematical Analysis and Applications, vol. 136, no. 1, pp. 29–38, 1988.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetX. Q. Yang, “Generalized convex functions and vector variational inequalities,” Journal of Optimization Theory and Applications, vol. 79, no. 3, pp. 563–580, 1993.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetX. M. Yang, X. Q. Yang, and K. L. Teo, “Generalized invexity and generalized invariant monotonicity,” Journal of Optimization Theory and Applications, vol. 117, no. 3, pp. 607–625, 2003.
View at: Publisher Site | Google Scholar | MathSciNetX. M. Yang, X. Q. Yang, and K. L. Teo, “Criteria for generalized invex monotonicities,” European Journal of Operational Research, vol. 164, no. 1, pp. 115–119, 2005.
View at: Publisher Site | Google Scholar | MathSciNetD. L. Zhu and P. Marcotte, “Co-coercivity and its role in the convergence of iterative schemes for solving variational inequalities,” SIAM Journal on Optimization, vol. 6, no. 3, pp. 714–726, 1996.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet