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.
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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.
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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.
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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.
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