Mathematical Inequalities (inbunden)
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Chapman & Hall/CRC
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Mathematical Inequalities

A Perspective

Inbunden, Engelska, 2010-12-01
1102 kr
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Drawing on the authors' research work from the last ten years, Mathematical Inequalities: A Perspective gives readers a different viewpoint of the field. It discusses the importance of various mathematical inequalities in contemporary mathematics and how these inequalities are used in different applications, such as scientific modeling. The authors include numerous classical and recent results that are comprehensible to both experts and general scientists. They describe key inequalities for real or complex numbers and sequences in analysis, including the Abel; the Biernacki, Pidek, and Ryll-Nardzewski; Cebysev's; the Cauchy-Bunyakovsky-Schwarz; and De Bruijn's inequalities. They also focus on the role of integral inequalities, such as Hermite-Hadamard inequalities, in modern analysis. In addition, the book covers Schwarz, Bessel, Boas-Bellman, Bombieri, Kurepa, Buzano, Precupanu, Dunkl-William, and Gruss inequalities as well as generalizations of Hermite-Hadamard inequalities for isotonic linear and sublinear functionals. For each inequality presented, results are complemented with many unique remarks that reveal rich interconnections between the inequalities. These discussions create a natural platform for further research in applications and related fields.
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"Written by two leading experts in this subject, this book is both a text on a topic of current interest in inequalities and a great overview of the techniques and striking applications of the inequalities theory." -Dumitru Acu, Zentralblatt MATH 1298 "Cerone and Dragomir have successfully produced an extensive list of inequalities used in analysis. ... The writing is straightforward and the text often references results given elsewhere. ... Recommended." - J.R. Burke, CHOICE, December 2011 "... a well-written and welcome addition to the literature. ... to have the results in one place is a service to all interested parties." - P.S. Bullen, Mathematical Reviews, Issue 2011m "One of the most interesting aspects is many instances of 'reverses' ... a useful book if you are interested in its specific subject matter ..." - MAA Reviews, February 2011

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Övrig information

Pietro Cerone is a professor of mathematics at Victoria University, where he served as head of the School of Computer Science and Mathematics from 2003 to 2008. Dr. Cerone is on the editorial board of a dozen international journals and has published roughly 200 refereed works in the field. His research interests include mathematical modeling, population dynamics, and applications of mathematical inequalities. Sever S. Dragomir is a professor of mathematics and chair of the international Research Group in Mathematical Inequalities and Applications at Victoria University. Dr. Dragomir is an editorial board member of more than 30 international journals and has published over 600 research articles. His research in pure and applied mathematics encompasses classical mathematical analysis, operator theory, Banach spaces, coding, adaptive quadrature and cubature rules, differential equations, and game theory.


Discrete Inequalities An Elementary Inequality for Two Numbers An Elementary Inequality for Three Numbers A Weighted Inequality for Two Numbers The Abel Inequality The Biernacki, Pidek, and Ryll-Nardzewski (BPR) Inequality Cebysev's Inequality for Synchronous Sequences The Cauchy-Bunyakovsky-Schwarz (CBS) Inequality for Real Numbers The Andrica-Badea Inequality A Weighted Gruss-Type Inequality Andrica-Badea's Refinement of the Gruss Inequality Cebysev-Type Inequalities De Bruijn's Inequality Daykin-Eliezer-Carlitz's Inequality Wagner's Inequality The Polya-Szego Inequality The Cassels Inequality Holder's Inequality for Sequences of Real Numbers The Minkowski Inequality for Sequences of Real Numbers Jensen's Discrete Inequality A Converse of Jensen's Inequality for Differentiable Mappings The Petrovic Inequality for Convex Functions Bounds for the Jensen Functional in Terms of the Second Derivative Slater's Inequality for Convex Functions A Jensen-Type Inequality for Double Sums Integral Inequalities for Convex Functions The Hermite-Hadamard Integral Inequality Hermite-Hadamard Related Inequalities Hermite-Hadamard Inequality for Log-Convex Mappings Hermite-Hadamard Inequality for the Godnova-Levin Class of Functions The Hermite-Hadamard Inequality for Quasi-Convex Functions The Hermite-Hadamard Inequality for s-Convex Functions in the Orlicz Sense The Hermite-Hadamard Inequality for s-Convex Functions in the Breckner Sense Inequalities for Hadamard's Inferior and Superior Sums A Refinement of the Hermite-Hadamard Inequality for the Modulus Ostrowski and Trapezoid-Type Inequalities Ostrowski's Integral Inequality for Absolutely Continuous Mappings Ostrowski's Integral Inequality for Mappings of Bounded Variation Trapezoid Inequality for Functions of Bounded Variation Trapezoid Inequality for Monotonic Mappings Trapezoid Inequality for Absolutely Continuous Mappings Trapezoid Inequality in Terms of Second Derivatives Generalised Trapezoid Rule Involving nth Derivative Error Bounds A Refinement of Ostrowski's Inequality for the Cebysev Functional Ostrowski-Type Inequality with End Interval Means Multidimensional Integration via Ostrowski Dimension Reduction Multidimensional Integration via Trapezoid and Three Point Generators with Dimension Reduction Relationships between Ostrowski, Trapezoidal, and Cebysev Functionals Perturbed Trapezoidal and Midpoint Rules A Cebysev Functional and Some Ramifications Weighted Three Point Quadrature Rules Gruss-Type Inequalities and Related Results The Gruss Integral Inequality The Gruss-Cebysev Integral Inequality Karamata's Inequality Steffensen's Inequality Young's Inequality Gruss-Type Inequalities for the Stieltjes Integral of Bounded Integrands Gruss-Type Inequalities for the Stieltjes Integral of Lipschitzian Integrands Other Gruss-Type Inequalities for the Riemann-Stieltjes Integral Inequalities for Monotonic Integrators Generalisations of Steffensen's Inequality over Subintervals Inequalities in Inner Product Spaces Schwarz's Inequality in Inner Product Spaces A Conditional Refinement of the Schwarz Inequality The Duality Schwarz-Triangle Inequalities A Quadratic Reverse for the Schwarz Inequality A Reverse of the Simple Schwarz Inequality A Reverse of Bessel's Inequality Reverses for the Triangle Inequality in Inner Product Spaces The Boas-Bellman Inequality The Bombieri Inequality Kurepa's Inequality Buzano's Inequality A Generalisation of Buzano's Inequality Generalisations of Precupanu's Inequality The Dunkl-William Inequality The Gruss Inequality in Inner Product Spaces A Refinement of the Gruss Inequality in Inner Product Spaces Inequalities in Normed Linear Spaces and for Functionals A Multiplicative Reverse for the Continuous Triangle Inequality Additive Reverses for the Continuous Triangle Inequality Reverses of the Discrete Triangle Inequality in Normed Spaces Other Multiplicative Reverse