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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