Korean Journal of Mathematics

The Kangwon-Kyungki Mathematical Society (강원경기수학회)
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ON OPIAL-TYPE INEQUALITIES VIA A NEW GENERALIZED INTEGRAL OPERATOR

  • Farid, Ghulam (Department of Mathematics, COMSATS University Islamabad) ;
  • Mehboob, Yasir (Department of Mathematics, COMSATS University Islamabad)
  • Received : 2020.02.09
  • Accepted : 2021.05.24
  • Published : 2021.06.30
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Abstract

Opial inequality and its consequences are useful in establishing existence and uniqueness of solutions of initial and boundary value problems for differential and difference equations. In this paper we analyze Opial-type inequalities for convex functions. We have studied different versions of these inequalities for a generalized integral operator. Further difference of Opial-type inequalities are utilized to obtain generalized mean value theorems, which further produce various interesting derivations for fractional and conformable integral operators.

Keywords

Acknowledgement

This work was supported by the Dong-A University research fund.

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