Generalizations and refinements of three-tuple Diamond-Alpha integral Hölder’s inequality on time scales
نویسندگان
چکیده
منابع مشابه
Diamond-alpha Integral Inequalities on Time Scales
The theory of the calculus of variations was recently extended to the more general time scales setting, both for delta and nabla integrals. The primary purpose of this paper is to further extend the theory on time scales, by establishing some basic diamond-alpha dynamic integral inequalities. We prove generalized versions of Hölder, Cauchy-Schwarz, Minkowski, and Jensen’s inequalities. For the ...
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The theory and applications of dynamic derivatives on time scales have recently received considerable attention. The primary purpose of this paper is to give basic properties of diamond-α derivatives which are a linear combination of delta and nabla dynamic derivatives on time scales. We prove a generalized version of Jensen’s inequality on time scales via the diamond-α integral and present som...
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The objective of this paper is twofold: (i) to survey existing results of generalized polynomials on time scales, covering definitions and properties for both delta and nabla derivatives; (ii) to extend previous results by using the more general notion of diamond-alpha derivative on time scales. We introduce a new notion of combined-polynomial series on a time scale, as a convex linear combinat...
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The constant is the best possible. There is a vast literature which deals with alternative proofs, various generalizations and extensions, and numerous variants and applications in analysis of inequality (1.1); see [1, 2, 3, 5, 7, 9, 8, 10, 13, 14, 15, 16, 17, 18, 19] and the references given therein. According to Hardy (see [6, Theorem 349]), Carleman’s inequality was generalized as follows. I...
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ژورنال
عنوان ژورنال: Journal of Inequalities and Applications
سال: 2019
ISSN: 1029-242X
DOI: 10.1186/s13660-019-2271-8