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Author: Mark Aleksandrovich Krasnoselʹskiĭ
Publisher:
ISBN:
Category : Convex domains
Languages : en
Pages : 224
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Book Description
Author: Mark Aleksandrovich Krasnoselʹskiĭ
Publisher:
ISBN:
Category : Convex domains
Languages : en
Pages : 224
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Book Description
Author: Mark Aleksandrovich Krasnoselʹskiĭ
Publisher:
ISBN:
Category : Convex domains
Languages : en
Pages : 262
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Book Description
Author: Peter Kosmol
Publisher: Walter de Gruyter
ISBN: 3110250209
Category : Mathematics
Languages : en
Pages : 405
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Book Description
This is an essentially self-contained book on the theory of convex functions and convex optimization in Banach spaces, with a special interest in Orlicz spaces. Approximate algorithms based on the stability principles and the solution of the corresponding nonlinear equations are developed in this text. A synopsis of the geometry of Banach spaces, aspects of stability and the duality of different levels of differentiability and convexity is developed. A particular emphasis is placed on the geometrical aspects of strong solvability of a convex optimization problem: it turns out that this property is equivalent to local uniform convexity of the corresponding convex function. This treatise also provides a novel approach to the fundamental theorems of Variational Calculus based on the principle of pointwise minimization of the Lagrangian on the one hand and convexification by quadratic supplements using the classical Legendre-Ricatti equation on the other. The reader should be familiar with the concepts of mathematical analysis and linear algebra. Some awareness of the principles of measure theory will turn out to be helpful. The book is suitable for students of the second half of undergraduate studies, and it provides a rich set of material for a master course on linear and nonlinear functional analysis. Additionally it offers novel aspects at the advanced level. From the contents: Approximation and Polya Algorithms in Orlicz Spaces Convex Sets and Convex Functions Numerical Treatment of Non-linear Equations and Optimization Problems Stability and Two-stage Optimization Problems Orlicz Spaces, Orlicz Norm and Duality Differentiability and Convexity in Orlicz Spaces Variational Calculus
Author: J. Musielak
Publisher: Springer
ISBN: 3540386920
Category : Mathematics
Languages : en
Pages : 227
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Book Description
Author: Petteri Harjulehto
Publisher: Springer
ISBN: 303015100X
Category : Mathematics
Languages : en
Pages : 169
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Book Description
This book presents a systematic treatment of generalized Orlicz spaces (also known as Musielak–Orlicz spaces) with minimal assumptions on the generating Φ-function. It introduces and develops a technique centered on the use of equivalent Φ-functions. Results from classical functional analysis are presented in detail and new material is included on harmonic analysis. Extrapolation is used to prove, for example, the boundedness of Calderón–Zygmund operators. Finally, central results are provided for Sobolev spaces, including Poincaré and Sobolev–Poincaré inequalities in norm and modular forms. Primarily aimed at researchers and PhD students interested in Orlicz spaces or generalized Orlicz spaces, this book can be used as a basis for advanced graduate courses in analysis.
Author: G. G. Lorentz
Publisher:
ISBN:
Category : Function spaces
Languages : en
Pages : 16
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Book Description
Author: M.M. Rao
Publisher: CRC Press
ISBN: 9780824784782
Category : Mathematics
Languages : en
Pages : 472
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Book Description
A reference/text for mathematicians or students involved in analysis, differential equations, probability theory, and the study of integral operators where only Lebesgue spaces were used in the past. Updates and extends the pioneering work by Krasnosel'skii and Rutickii in their 1958 treatise on Orl
Author: M.M. Rao
Publisher: CRC Press
ISBN: 9780203910863
Category : Mathematics
Languages : en
Pages : 496
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Book Description
Presents previously unpublished material on the fundumental pronciples and properties of Orlicz sequence and function spaces. Examines the sample path behavior of stochastic processes. Provides practical applications in statistics and probability.
Author: Henryk Hudzik
Publisher: CRC Press
ISBN: 9780824704193
Category : Mathematics
Languages : en
Pages : 538
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Book Description
This volume compiles research results from the fifth Function Spaces International Conference, held in Poznan, Poland. It presents key advances, modern applications and analyses of function spaces and contains two special sections recognizing the contributions and influence of Wladyslaw Orlicz and Genadil Lozanowskii.
Author: Constantin P. Niculescu
Publisher: Springer
ISBN: 3319783378
Category : Mathematics
Languages : en
Pages : 415
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Book Description
Thorough introduction to an important area of mathematics Contains recent results Includes many exercises
