Research article

On an integral and consequent fractional integral operators via generalized convexity

  • Received: 28 May 2020 Accepted: 27 July 2020 Published: 25 September 2020
  • MSC : 26D10, 31A10, 26A33

  • Fractional calculus operators are very useful in basic sciences and engineering. In this paper we study an integral operator which is directly related with many known fractional integral operators. A new generalized convexity namely exponentially (α, h?m)-convexity is defined which has been applied to obtain the bounds of unified integral operators. A generalized Hadamard inequality is established for the generalized convex functions. The established theorems reproduce several known results.

    Citation: Wenfeng He, Ghulam Farid, Kahkashan Mahreen, Moquddsa Zahra, Nana Chen. On an integral and consequent fractional integral operators via generalized convexity[J]. AIMS Mathematics, 2020, 5(6): 7632-7648. doi: 10.3934/math.2020488

    Related Papers:

  • Fractional calculus operators are very useful in basic sciences and engineering. In this paper we study an integral operator which is directly related with many known fractional integral operators. A new generalized convexity namely exponentially (α, h?m)-convexity is defined which has been applied to obtain the bounds of unified integral operators. A generalized Hadamard inequality is established for the generalized convex functions. The established theorems reproduce several known results.


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  • © 2020 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
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