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Some properties of semi-\(E\)-convex functions. (English) Zbl 1072.90561

Summary: In this paper, we show that Theorems 4.2, 4.3 and 4.6 in [E. A. Youness, J. Optim. Theory Appl. 102, No. 2, 439–450 (1999; Zbl 0937.90082)] are incorrect by giving some counterexamples. We introduce a new class of semi-\(E\)-convex function and discuss some its basic properties.

MSC:

90C26 Nonconvex programming, global optimization
26B25 Convexity of real functions of several variables, generalizations

Citations:

Zbl 0937.90082
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References:

[1] Youness, E.A., E-convex sets, E-convex functions, and E-convex programming, J. optim. theory appl., 102, 439-450, (1999) · Zbl 0937.90082
[2] Noor, M.A., New approximation schemes for general variational inequalities, J. math. anal. appl., 251, 217-229, (2000) · Zbl 0964.49007
[3] Noor, M.A., Fuzzy preinvex functions, Fuzzy sets and systems, 64, 95-104, (1994) · Zbl 0844.90111
[4] Abou-Tair, I.A.; Sulaiman, W.T., Inequalities via convex functions, Internat. J. math. math. sci., 22, 543-546, (1999) · Zbl 0965.26012
[5] Yang, X.M., On E-convex set, E-convex function and E-convex programming, J. optim. theory appl., 109, 699-703, (2001) · Zbl 1068.90592
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