Some new inequalities of the Ostrowski-Grüss, Čebyšev, and Trapezoid types on time scales

Volume 12, Issue 4, pp 192--205 http://dx.doi.org/10.22436/jnsa.012.04.01

Publication Date: December 05, 2018 Submission Date: October 24, 2018 Revision Date: November 12, 2018 Accteptance Date: November 15, 2018

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Authors

Eze R. Nwaeze - Department of Mathematics, Tuskegee University, Tuskegee, AL 36088, USA. Nurhan Kaplan - Art and Science Faculty, Mathematics Department, Niğde Ömer Halisdemir University, Niğde, Turkey. Fatma Gozde Tuna - Art and Science Faculty, Mathematics Department, Niğde Ömer Halisdemir University, Niğde, Turkey. Adnan Tuna - Art and Science Faculty, Mathematics Department, Niğde Ömer Halisdemir University, Niğde, Turkey.

Abstract

In this paper, we establish some novel Ostrowski-Grüss, Čebyšev, and Trapezoid type inequalities involving functions whose second derivatives are bounded on time scales. We also give some other interesting inequalities as special cases of our results.

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Keywords

• Ostrowski's inequality
• Čebyšev inequality
• Ostrowski-Grüss
• Trapezoid inequality
• time scales

MSC

•  26D15
•  54C30
•  26D10

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