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Discrete Fractional Hermite-Hadamard Inequality

This thesis is comprised of three main parts: The Hermite-Hadamard inequality on discrete time scales, the fractional Hermite-Hadamard inequality, and Karush-Kuhn- Tucker conditions on higher dimensional discrete domains. In the first part of the thesis, Chapters 2 & 3, we define a convex function on a special time scale T where all the time points are not uniformly distributed on a time line. With the use of the substitution rules of integration we prove the Hermite-Hadamard inequality for convex functions defined on T. In the fourth chapter, we introduce fractional order Hermite-Hadamard inequality and characterize convexity in terms of this inequality. In the fifth chapter, we discuss convexity on n{dimensional discrete time scales T = T1 × T2 × ... × Tn where Ti ⊂ R , i = 1; 2,…,n are discrete time scales which are not necessarily periodic. We introduce the discrete analogues of the fundamental concepts of real convex optimization such as convexity of a function, subgradients, and the Karush-Kuhn-Tucker conditions.
We close this thesis by two remarks for the future direction of the research in this area.

Identiferoai:union.ndltd.org:WKU/oai:digitalcommons.wku.edu:theses-2942
Date01 April 2017
CreatorsArslan, Aykut
PublisherTopSCHOLAR®
Source SetsWestern Kentucky University Theses
Detected LanguageEnglish
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