Hermite-Hadamard-Fejér Inequality Related to Generalized Convex Functions via Fractional Integrals
Hermite-Hadamard-Fejér Inequality Related to Generalized Convex Functions via Fractional Integrals
This paper deals with Hermite-Hadamard-Fejér inequality for <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mrow><mml:mi>η</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>η</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:math>-convex functions via fractional integrals. Some mid-point and trapezoid type inequalities related to Hermite-Hadamard inequality when the absolute value of derivative of considered function is <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M2"><mml:mo stretchy="false">(</mml:mo><mml:msub><mml:mrow><mml:mi>η</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant="normal">1</mml:mn></mml:mrow></mml:msub><mml:mo>,</mml:mo><mml:msub><mml:mrow><mml:mi>η</mml:mi></mml:mrow><mml:mrow><mml:mn mathvariant="normal">2</mml:mn></mml:mrow></mml:msub><mml:mo stretchy="false">)</mml:mo></mml:math>-convex functions are obtained. Furthermore, a …