New Bounds of Ostrowski-Gruss Type Inequality for (k + 1) Points on Time Scales

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Eze R. Nwaeze, Seth Kermausuor, New Bounds of Ostrowski-Gruss Type Inequality for (k + 1) Points on Time Scales, Int. J. Anal. Appl., 15 (2) (2017), 211-221.

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Eze R. Nwaeze, Seth Kermausuor

Abstract

The aim of this paper is to present three new bounds of the Ostrowski--Gr\"uss type inequality for points $x_0,x_1,x_2,\cdots,x_k$ on time scales. Our results generalize result of Ng\^o and Liu, and extend results of Ujevi\'c to time scales with $(k+1)$ points. We apply our results to the continuous, discrete, and quantum calculus to obtain many new interesting inequalities. An example is also considered. The estimates obtained in this paper will be very useful in numerical integration especially for the continuous case.

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