Research article

Boundedness of fractional integral operators containing Mittag-Leffler functions via (s,m)-convexity

  • Received: 09 October 2019 Accepted: 14 December 2019 Published: 08 January 2020
  • MSC : 26A51, 26A33, 33E12

  • The objective of this paper is to derive the bounds of fractional integral operators which contain Mittag-Leffler functions in the kernels. By using (s, m)-convex functions bounds of these operators are evaluated which lead to obtain their boundedness and continuity. Moreover the presented results can be used to get various results for known fractional integrals and functions deducible from (s, m)-convexity. Also a version of Hadamard type inequality is established for (s, m)-convex functions via generalized fractional integrals.

    Citation: Ghulam Farid, Saira Bano Akbar, Shafiq Ur Rehman, Josip Pečarić. Boundedness of fractional integral operators containing Mittag-Leffler functions via (s,m)-convexity[J]. AIMS Mathematics, 2020, 5(2): 966-978. doi: 10.3934/math.2020067

    Related Papers:

  • The objective of this paper is to derive the bounds of fractional integral operators which contain Mittag-Leffler functions in the kernels. By using (s, m)-convex functions bounds of these operators are evaluated which lead to obtain their boundedness and continuity. Moreover the presented results can be used to get various results for known fractional integrals and functions deducible from (s, m)-convexity. Also a version of Hadamard type inequality is established for (s, m)-convex functions via generalized fractional integrals.


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