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

M. Emin Özdemir; Saad I. Butt; Bahtiyar Bayraktar; Jamshed Nasir; M. Emin Özdemir; Saad I. Butt; Bahtiyar Bayraktar; Jamshed Nasir

doi:10.3934/math.2020253

AIMS Mathematics

2020, Volume 5, Issue 4: 3906-3921. doi: 10.3934/math.2020253

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Research article

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

Received: 11 December 2019 Accepted: 03 April 2020 Published: 26 April 2020
MSC : 26A51, 26D15

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

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Abstract

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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