Generalized fractional integral inequalities for exponentially $(s,m)$-convex functions
Xiaoli Qiang, Ghulam Farid, Josip Pečarić, Saira Bano Akbar
Abstract
Abstract In this paper we have derived the fractional integral inequalities by defining exponentially $(s,m)$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>(</mml:mo><mml:mi>s</mml:mi><mml:mo>,</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo></mml:math> -convex functions. These inequalities provide upper bounds, boundedness, continuity, and Hadamard type inequality for fractional integrals containing an extended Mittag-Leffler function. The results about fractional integral operators for s -convex, m -convex, $(s,m)$ <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML"><mml:mo>(</mml:mo><mml:mi>s</mml:mi><mml:mo>,</mml:mo><mml:mi>m</mml:mi><mml:mo>)</mml:mo></mml:math> -convex, exponentially convex, exponentially s -convex, and convex functions are direct consequences of presented results.