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On strongly \(\alpha\)-preinvex functions. (English) Zbl 1121.26010
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)].

MSC:
26B25 Convexity of real functions of several variables, generalizations
90C25 Convex programming
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