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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.
Table des matières
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.
Résumé
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.
Texte suppl.
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)
Commentaire
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)
