Korean J. Math.  Vol 29, No 2 (2021)  pp.227-237
DOI: https://doi.org/10.11568/kjm.2021.29.2.227

On Opial-type inequalities via a new generalized integral operator

Ghulam Farid, Yasir Mehboob

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


Convex function, Opial inequality, Integral operators, Fractional integral operators, Conformable integral operators

Subject classification

26A51, 26A33, 33E12

Sponsor(s)



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References


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