Fractional generalized Hadamard and Fejér-Hadamard inequalities for <em>m</em>-convex functions

Xiuzhi Yang; G. Farid; Waqas Nazeer; Muhammad Yussouf; Yu-Ming Chu; Chunfa Dong; Xiuzhi Yang; G. Farid; Waqas Nazeer; Muhammad Yussouf; Yu-Ming Chu; Chunfa Dong

doi:10.3934/math.2020407

AIMS Mathematics

2020, Volume 5, Issue 6: 6325-6340. doi: 10.3934/math.2020407

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Research article

Fractional generalized Hadamard and Fejér-Hadamard inequalities for m-convex functions

1.
School of Mechanical and Electrical, Hubei Polytechnic University, Huangshi, 435003, China
2.
Department of Mathematics, COMSATS University Islamabad, Attock Campus, Pakistan
3.
Department of Mathematics, GC University, Lahore, Pakistan
4.
Department of Mathematics, University of Sargodha, Sargodha, Pakistan
5.
Department of Mathematics, Huzhou University, Huzhou, 313000, P. R. China
6.
Hunan Provincial Key Laboratory of Mathematical Modeling and Analysis in Engineering, Changsha University of Science & Technology, Changsha, 410114, P. R. China
7.
School of Mechanical and Electrical, Hubei Polytechnic University, Huangshi, 435003, China

Received: 12 June 2020 Accepted: 27 July 2020 Published: 07 August 2020
MSC : 26A51, 26A33, 33E12

The objective of this paper is to present the fractional Hadamard and Fejér-Hadamard inequalities in generalized forms. By employing a generalized fractional integral operator containing extended generalized Mittag-Leffler function involving a monotone increasing function, we generalize the well known fractional Hadamard and Fejér-Hadamard inequalities for m-convex functions. Also we study the error bounds of these generalized inequalities. In connection with some published results from presented inequalities are obtained.
Citation: Xiuzhi Yang, G. Farid, Waqas Nazeer, Muhammad Yussouf, Yu-Ming Chu, Chunfa Dong. Fractional generalized Hadamard and Fejér-Hadamard inequalities for m-convex functions[J]. AIMS Mathematics, 2020, 5(6): 6325-6340. doi: 10.3934/math.2020407

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Abstract

The objective of this paper is to present the fractional Hadamard and Fejér-Hadamard inequalities in generalized forms. By employing a generalized fractional integral operator containing extended generalized Mittag-Leffler function involving a monotone increasing function, we generalize the well known fractional Hadamard and Fejér-Hadamard inequalities for m-convex functions. Also we study the error bounds of these generalized inequalities. In connection with some published results from presented inequalities are obtained.

References

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