Overview

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.

Full Product Details

Author:   George Isac ,  Sándor Zoltán Németh
Publisher:   Springer-Verlag New York Inc.
Imprint:   Springer-Verlag New York Inc.
Edition:   Softcover reprint of hardcover 1st ed. 2008
Volume:   13
Dimensions:   Width: 15.50cm , Height: 1.30cm , Length: 23.50cm
Weight:   0.454kg
ISBN:  

9781441944849

ISBN 10:   1441944842
Pages:   245
Publication Date:   08 December 2010
Audience:   Professional and scholarly ,  Professional & Vocational ,  Postgraduate, Research & Scholarly
Format:   Paperback
Publisher's Status:   Active
Availability:   In Print  
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Table of Contents

Scalar Derivatives in Euclidean Spaces.- Asymptotic Derivatives and Asymptotic Scalar Derivatives.- Scalar Derivatives in Hilbert Spaces.- Scalar Derivatives in Banach Spaces.- Monotone Vector Fields on Riemannian Manifolds and Scalar Derivatives.

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 ZAElinescu, Mathematical Reviews, Issue 2010 a)

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 Zalinescu, Mathematical Reviews, Issue 2010 a)

"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)"

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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