• Bulletin of the Korean Mathematical Society
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• v.49 no.6
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• pp.1263-1274
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• 2012

In the present paper we establish some new Opial-type inequalities involving higher order partial derivatives. The results in special cases yield some of the recent results on Opial's inequality and provide new estimates on inequalities of this type.

• Korean Journal of Mathematics
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• v.29 no.2
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• pp.227-237
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• 2021

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.

• The Pure and Applied Mathematics
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• v.22 no.4
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• pp.315-331
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• 2015

The purpose of this paper is to obtain Opial-type inequalities that are useful to study various qualitative properties of certain differential equations involving impulses. After we obtain some Opial-type inequalities, we apply our results to certain differential equations involving impulses.

• Korean Journal of Mathematics
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• v.28 no.4
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• pp.717-737
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• 2020

In this paper, we establish some weighted generalization of Opial type inequalities in two independent variables for two functions. We also obtain weighted Opial type inequalities by using p-norms. Special cases of our results reduce to the inequalities in earlier study.

• Kyungpook Mathematical Journal
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• v.51 no.2
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• pp.165-175
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• 2011

The purpose of this note is to give Opial type inequalities with nonlocal conditions. Also, a reverse of the original inequality with y(a) = y(b) = 0 is derived. We apply these inequalities to second-order differential equations with nonlocal conditions to derive several necessary conditions for the existence of solutions.