Scalar and Asymptotic Scalar Derivatives: Theory and Applications Softcover reprint of hardcover 1st ed. 2008 Edition

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)

This book is devoted to the study of scalar and asymptotic scalar derivatives and their applications to some problems in nonlinear analysis, Riemannian geometry, and applied mathematics. The theoretical results are developed in particular with respect to the study of complementarity problems, monotonicity of nonlinear mappings ,and non-gradient type monotonicity on Riemannian manifolds. Scalar and Asymptotic Derivatives: Theory and Applications also presents the material in relation to Euclidean spaces, Hilbert spaces, Banach spaces, Riemannian manifolds, and Hadamard manifolds.

This book is intended for researchers and graduate students working in the fields of nonlinear analysis, Riemannian geometry, and applied mathematics. In addition, it fills a gap in the literature as the first book to appear on the subject.