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Opial and Pólya type inequalities via convexity

Saker S. H., Abdou D. M., Kubiaczyk I.

Fasciculi Mathematici

2018

Nr 60

145--159

In this paper, we prove some new dynamic inequalities related to Opial and Pólya type inequalities on a time scale T. We will derive the integral and discrete inequalities of Polya’s type as special cases and also derive several classical integral inequalities of Opial’s type that has been obtained in the literature as special cases. The main results will be proved by using the chain rule, Hölder’s inequality and Jensen’s inequality, Taylor formula on time scales.

On Hermite-Hadamard type inequalities for functions whose first derivative absolute values are convex and concave

Qaisar S., Hussain S.

Fasciculi Mathematici

2017

Nr 58

155--166

In this paper, we derive general integral identity by establishing new Hermite-Hadamard type inequalities for functions whose absolute values of derivatives are convex and concave. Corresponding error estimates for midpoint formula are also included. Moreover, some applications to special means of real numbers are also provided.

Some new factor theorem for absolute summability

Sulaiman W. T.

Demonstratio Mathematica

2013

Vol. 46, nr 1

149--156

A new general theorem concerning some kind of absolute summability is presented.

A further generalization of Hardy-Hilbert's integral inequality with parameter and applications

He L., Dragomir S. S., Yang Q.

Journal of Applied Analysis

2006

Vol. 12, nr 1

59-70

In this paper, by introducing some parameters and by employing a sharpening of Hölder's inequality, a new generalization of Hardy-Hilbert integral inequality involving the Beta function is established. At the same time, an extension of Widder's theorem is given.

Integral inequalities of Wirtinger and Opial type in three independent variables

Pachpatte B. G.

Fasciculi Mathematici

1999

Nr 30

113-129

In the present paper we establish some new Wirtinger and Opial type integral inequalities involving functions of three independent variables and their partial derivatives. The method used in the proof is elementary and our results provide new estimates on inequalities ofthis type.