AIMS Mathematics, 2020, 5(4): 3906-3921. doi: 10.3934/math.2020253.

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Several integral inequalities for (α, s,m)-convex functions

1 Bursa Uludağ University, Department of Mathematics and Science Education, 16059, BURSA, Turkey
2 COMSATS University Islamabad, Lahore Campus, Pakistan

In this paper, we establish several new integral inequalities for (α, s,m)-convex functions. We recapture the Hermite-Hadamard inequality as a particular case. In order to obtain our results, we use classical inequalities such as Hölder inequality, Hölder-Işcan inequality and Power mean inequality. We formulate several bounds involving special functions like classical Euler-Gamma, Beta and PsiGamma functions. We also give some applications.
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Keywords convex function; (α, s,m)-convex function; Hermite-Hadamard inequality; Riemann-Liouville fractional integrals; Hölder’s inequality; power mean inequality; Psi-Gamma functions

Citation: M. Emin Özdemir, Saad I. Butt, Bahtiyar Bayraktar, Jamshed Nasir. Several integral inequalities for (α, s,m)-convex functions. AIMS Mathematics, 2020, 5(4): 3906-3921. doi: 10.3934/math.2020253

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