Research article

Fractional integral versions of Hermite-Hadamard type inequality for generalized exponentially convexity

  • Received: 20 May 2020 Accepted: 17 July 2020 Published: 23 July 2020
  • MSC : 26B25, 26A33, 26A51, 33E12

  • In this paper, we establish generalized fractional versions of Hermite-Hadamard inequalities for exponentially (α, h - m)-convex functions, exponentially (h - m)-convex functions and exponentially (α, m)-convex functions. These inequalities arise when using the generalized fractional integral operators containing Mittag-Leffler function via a monotonically increasing function. The presented results hold at the same time for various kinds of convexities and well-known fractional integral operators. Moreover, the established inequalities reproduce several known results which are part of the existing literature.

    Citation: Hengxiao Qi, Muhammad Yussouf, Sajid Mehmood, Yu-Ming Chu, Ghulam Farid. Fractional integral versions of Hermite-Hadamard type inequality for generalized exponentially convexity[J]. AIMS Mathematics, 2020, 5(6): 6030-6042. doi: 10.3934/math.2020386

    Related Papers:

  • In this paper, we establish generalized fractional versions of Hermite-Hadamard inequalities for exponentially (α, h - m)-convex functions, exponentially (h - m)-convex functions and exponentially (α, m)-convex functions. These inequalities arise when using the generalized fractional integral operators containing Mittag-Leffler function via a monotonically increasing function. The presented results hold at the same time for various kinds of convexities and well-known fractional integral operators. Moreover, the established inequalities reproduce several known results which are part of the existing literature.


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