Riemann-Liouville Fractional integral operators with respect to increasing functions and strongly $ (\alpha, m) $-convex functions

Ghulam Farid; Hafsa Yasmeen; Hijaz Ahmad; Chahn Yong Jung; Ghulam Farid; Hafsa Yasmeen; Hijaz Ahmad; Chahn Yong Jung

doi:10.3934/math.2021661

AIMS Mathematics

2021, Volume 6, Issue 10: 11403-11424. doi: 10.3934/math.2021661

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Research article

Riemann-Liouville Fractional integral operators with respect to increasing functions and strongly $ (\alpha, m) $-convex functions

1.
Department of Mathematics, COMSATS University Islamabad, Attock Campus, Pakistan
2.
Department of Basic Sciences, University of Engineering and Technology, Peshawar, Pakistan
3.
Department of Business Administration, Gyeongsang National University Jinju 52828, Korea

Received: 11 January 2021 Accepted: 18 July 2021 Published: 09 August 2021
MSC : 26A51, 26A33, 33E12

In this paper Hadamard type inequalities for strongly $ (\alpha, m) $-convex functions via generalized Riemann-Liouville fractional integrals are studied. These inequalities provide generalizations as well as refinements of several well known inequalities. The established results are further connected with fractional integral inequalities for Riemann-Liouville fractional integrals of convex, strongly convex and strongly $ m $-convex functions. By using two fractional integral identities some more Hadamard type inequalities are proved.
- $ (\alpha, m) $-convex function,
- strongly $ (\alpha, m) $-convex function,
- Hadamard inequality,
- Riemann-Liouville fractional integrals
Citation: Ghulam Farid, Hafsa Yasmeen, Hijaz Ahmad, Chahn Yong Jung. Riemann-Liouville Fractional integral operators with respect to increasing functions and strongly $ (\alpha, m) $-convex functions[J]. AIMS Mathematics, 2021, 6(10): 11403-11424. doi: 10.3934/math.2021661

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Abstract

In this paper Hadamard type inequalities for strongly $ (\alpha, m) $-convex functions via generalized Riemann-Liouville fractional integrals are studied. These inequalities provide generalizations as well as refinements of several well known inequalities. The established results are further connected with fractional integral inequalities for Riemann-Liouville fractional integrals of convex, strongly convex and strongly $ m $-convex functions. By using two fractional integral identities some more Hadamard type inequalities are proved.

References

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