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Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 32, No. 1, pp. 79-87 (2016)
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Integral inequalities of Hermite-Hadamard type for functions whose derivatives are strongly $\alpha$-preinvex

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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

**Full text of the article:**

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FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition
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