Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 32, No. 1, pp. 79-87 (2016)

Integral inequalities of Hermite-Hadamard type for functions whose derivatives are strongly $\alpha$-preinvex

Yan Wang, Bo-Yan Xi and Feng Qi

Inner Mongolia University for Nationalities, Inner Mongolia University for Nationalities and Tianjin Polytechnic University

Abstract: In the paper, the authors introduce a new notion "strongly $\alpha$-preinvex function", establish an integral identity for the newly introduced function, and find some Hermite-Hadamard type integral inequalities for a function that the power of the absolute value of its first derivative is strongly $\alpha$-preinvex.

Keywords: Hermite-Hadamard type integral inequalities; invex set; strongly $\alpha$-preinvex function

Classification (MSC2000): 26D15; 26A51, 26B12, 41A55

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