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EXTENSIONS OF THE HERMITE–HADAMARD INEQUALITY FOR $r$-PREINVEX FUNCTIONS ON AN INVEX SET
Part of:
Inequalities
Published online by Cambridge University Press: 06 March 2017
Abstract
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Necessary and sufficient conditions to characterise weakly $r$-preinvex functions on an invex set are obtained and used to establish generalisations of the Hermite–Hadamard inequality for such functions.
MSC classification
Secondary:
90C25: Convex programming
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- Research Article
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- © 2017 Australian Mathematical Publishing Association Inc.
References
Antczak, T., ‘
r-preinvexity and r-invexity in mathematical programming’, Comput. Math. Appl.
50(3–4) (2005), 551–566.Google Scholar
Antczak, T., ‘A new method of solving nonlinear mathematical programming problems involving r-invex functions’, J. Math. Anal. Appl.
311(1) (2005), 313–323.Google Scholar
Antczak, T., ‘Mean value in invexity analysis’, Nonlinear Anal.
60 (2005), 1473–1484.CrossRefGoogle Scholar
Ben-Israel, A. and Mond, B., ‘What is invexity?’, J. Aust. Math. Soc. Ser. B
28 (1986), 1–9.Google Scholar
Hanson, M. A., ‘On sufficiency of the Kuhn–Tucker conditions’, J. Math. Anal. Appl.
80(2) (1981), 545–550.Google Scholar
Mitrinović, D. S., Pečarić, J. E. and Fink, A. M., Classical and New Inequalities in Analysis (Kluwer Academic, Dordrecht, 1993).Google Scholar
Mohan, S. R. and Neogy, S. K., ‘On invex sets and preinvex functions’, J. Math. Anal. Appl.
189 (1995), 901–908.Google Scholar
Noor, M. A., ‘Invex equilibrium problems’, J. Math. Anal. Appl.
302(2) (2005), 463–475.CrossRefGoogle Scholar
Noor, M. A., ‘Hermite–Hadamard integral inequalities for log-preinvex functions’, J. Math. Anal. Approx. Theory
2(2) (2007), 126–131.Google Scholar
Ul-Haq, W. and Iqbal, J., ‘Hermite–Hadamard-type inequalities for r-preinvex functions’, J. Appl. Math.
2013 (2013), Article ID 126457, 5 pages.Google Scholar
Weir, T. and Mond, B., ‘Pre-invex functions in multiple objective optimization’, J. Math. Anal. Appl.
136(1) (1988), 29–38.Google Scholar
Yang, X. M., Yang, X. Q. and Teo, K. L., ‘Characterizations and applications of prequasi-invex functions’, J. Optim. Theory Appl.
110(3) (2001), 645–668.Google Scholar
Zhao, K.-Q., Long, P.-J. and Wan, X., ‘A characterization for r-preinvex function’, J. Chongqing Normal University (Natural Science)
28(2) (2011), 1–5.Google Scholar
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