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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We study diamond-alpha integrals on time scales. A diamond-alpha version of Fermat’s theorem for stationary points is also proved, as well as Rolle’s, Lagrange’s, and Cauchy’s mean value theorems on time scales. Mathematics Subject Classification 2000: 26A42; 39A12.
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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 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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ژورنال
عنوان ژورنال: Bulletin of the Malaysian Mathematical Sciences Society
سال: 2014
ISSN: 0126-6705,2180-4206
DOI: 10.1007/s40840-014-0096-7