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Discontinuity, Nonlinearity, and Complexity

Dimitry Volchenkov (editor), Dumitru Baleanu (editor)

Dimitry Volchenkov(editor)

Mathematics & Statistics, Texas Tech University, 1108 Memorial Circle, Lubbock, TX 79409, USA


Dumitru Baleanu (editor)

Cankaya University, Ankara, Turkey; Institute of Space Sciences, Magurele-Bucharest, Romania


Vectorial Inequalities for Integral Operators Involving Ratios of Functions and Convexity

Discontinuity, Nonlinearity, and Complexity 1(3) (2012) 279--304 | DOI:10.5890/DNC.2012.08.001

George A. Anastassiou

Department of Mathematical Sciences, University of Memphis , Memphis, TN 38152, U.S.A.

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Here we present vectorial integral inequalities for products of multivariate convex and increasing functions applied to vectors of ratios of functions. As applications we derive a wide range of vectorial fractional inequalities of Hardy type. They involve the left and right Riemann-Liouville fractional integrals and their generalizations, in particular the Hadamard fractional integrals. Also inequalities for Riemann-Liouville, Caputo, Canavati and their generalizations fractional derivatives. These application inequalities are of Lp type, p ≥ 1, and exponential type.


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