Fan, Liya; Guo, Yunlian On strongly \(\alpha\)-preinvex functions. (English) Zbl 1121.26010 J. Math. Anal. Appl. 330, No. 2, 1412-1425 (2007). Authors’ abstract: By means of a series of counterexamples, the authors study in a systematic way the relationships among (pseudo, quasi) \(\alpha\)-preinvexity, (strict, strong, pseudo, quasi) \(\alpha \)-invexity and (strict, strong, pseudo, quasi) \(\alpha \eta\)-monotonicity. Results obtained in this paper can be viewed as a refinement and improvement of the results of M. A. Noor and K. I. Noor [J. Math. Anal. Appl. 316, No. 2, 697–706 (2006; Zbl 1093.26006)]. Reviewer: Ştefan Mititelu (Bucureşti) Cited in 6 Documents MSC: 26B25 Convexity of real functions of several variables, generalizations 90C25 Convex programming Keywords:relations; (pseudo, quasi) \(\alpha\)-preinvexity; (pseudo, quasi) \(\alpha\)-invexity; (pseudo, quasi) \(\alpha \eta\)-monotonicity PDF BibTeX XML Cite \textit{L. Fan} and \textit{Y. Guo}, J. Math. Anal. Appl. 330, No. 2, 1412--1425 (2007; Zbl 1121.26010) Full Text: DOI References: [1] Noor, M.A., Invex equilibrium problems, J. math. anal. appl., 302, 463-475, (2005) · Zbl 1058.49007 [2] Noor, M.A.; Noor, K.I., Hemiequilibrium-like problems, Nonlinear anal., 64, 12, 2631-2642, (2006) · Zbl 1119.49011 [3] Noor, M.A., Invex &z.epsiv;-equilibrium problems with trifunction, Int. J. pure appl. math., 13, 123-136, (2004) · Zbl 1045.49014 [4] Ruiz-Garzon, G.; Osuna-Gomez, P.; Rufian-Lizana, A., Generalized invex monotonicity, European J. oper. res., 144, 501-512, (2003) · Zbl 1028.90036 [5] Yang, X.M.; Yang, X.Q.; Teo, K.L., Generalized invexity and generalized invariant monotonicity, J. optim. theory appl., 117, 607-625, (2003) · Zbl 1141.90504 [6] Mohan, S.R.; Neogy, S.K., On invex sets and preinvex functions, J. math. anal. appl., 189, 901-908, (1995) · Zbl 0831.90097 [7] Noor, M.A.; Noor, K.I., Some characterizations of strongly preinvex functions, J. math. anal. appl., 316, 697-706, (2006) · Zbl 1093.26006 [8] Weir, T.; Mond, B., Preinvex functions in multiobjective optimization, J. math. anal. appl., 136, 29-38, (1988) · Zbl 0663.90087 [9] Noor, M.A., On generalized preinvex functions and monotonicities, J. ineq. pure appl. math., 5, 4, 1-9, (2004), Article 110 · Zbl 1094.26008 This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.