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AIMS Mathematics

2020, Volume 5, Issue 6: 7632-7648. doi: 10.3934/math.2020488
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Research article

On an integral and consequent fractional integral operators via generalized convexity

  • 1.
    College of Science, Hainan University , Haikou, Hainan, 570228, China
  • 2.
    Department of Mathematics, COMSATS University Islamabad, Attock Campus, Pakistan
  • 3.
    Department of Mathematics, University of Wah, Wah Cant, Pakistan
  • 4.
    Faculty of Network, Haikou College of Economics, Haikou, Hainan, 571127, China
  • 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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