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Scalar and Asymptotic Scalar Derivatives

Theory and Applications

  • Book
  • © 2008

Overview

Authors:
  1. Sándor Zoltán Németh
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    You can also search for this author in PubMed   Google Scholar

  2. George Isac
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    You can also search for this author in PubMed   Google Scholar

  • Presents the theory and applications of scalar and asymptotic derivatives
  • Systematic, clear and coherent presentation
  • Includes supplementary material: sn.pub/extras

Part of the book series: Springer Optimization and Its Applications (SOIA, volume 13)

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Table of contents (5 chapters)

  1. Front Matter

    Pages 1-12
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  2. Scalar Derivatives in Euclidean Spaces

    • George Isac, Sándor Zoltán Németh
    Pages 1-29

  3. Asymptotic Derivatives and Asymptotic Scalar Derivatives

    • George Isac, Sándor Zoltán Németh
    Pages 31-77

  4. Scalar Derivatives in Hilbert Spaces

    • George Isac, Sándor Zoltán Németh
    Pages 79-160

  5. Scalar Derivatives in Banach Spaces

    • George Isac, Sándor Zoltán Németh
    Pages 161-177

  6. Monotone Vector Fields on Riemannian Manifolds and Scalar Derivatives

    • George Isac, Sándor Zoltán Németh
    Pages 179-229

  7. Back Matter

    Pages 1-14
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Keywords

About this book

This book is devoted to the study of scalar and asymptotic scalar derivatives and their applications to the study of some problems considered in nonlinear analysis, in geometry, and in applied mathematics. The notion of a scalar derivative is due to S. Z. Nemeth, ´ and the notion of an asymptotic scalar derivative is due to G. Isac. Both notions are recent, never considered in a book, and have interesting applications. About applications, we cite applications to the study of complementarity problems, to the study of xed points of nonlinear mappings, to spectral nonlinear analysis, and to the study of some interesting problems considered in differential geometry and other applications. A new characterization of monotonicity of nonlinear mappings is another remarkable application of scalar derivatives. A relation between scalar derivatives and asymptotic scalar derivatives, - alized by an inversion operator is also presented in this book. This relation has important consequences in the theory of scalar derivatives, and in some applications. For example, this relation permitted us a new development of the method of exceptional family of elements, introduced and used by G. Isac in complementarity theory. Now, we present a brief description of the contents of this book. Chapter 1 is dedicated to the study of scalar derivatives in Euclidean spaces.

Reviews

From the reviews:

"The scalar derivative … provided this limit exists and is finite, a notion introduced and studied by the second author of this book. … Based mainly on recent results obtained by the authors, appearing for the first time in book form, this volume is a valuable contribution to the field. It can be recommended to researchers and graduate students working in nonlinear analysis, fixed point theory, optimization, Riemannian geometry, and applied mathematics." (Stefan Cobzas, Zentralblatt MATH, Vol. 1159, 2009)

“The aim of this book is to provide a systematic study of scalar and asymptotic scalar derivatives and to point out several applications of them. … The book also contains a list of approximately 190 references, an index and a preface. … the book is the first in the literature on the subject and is addressed to graduate students at an advanced level and to researchers and practitioners in the fields of nonlinear analysis, Riemannian geometry and applied mathematics.” (Constantin Zălinescu, Mathematical Reviews, Issue 2010 a)

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