Theory of Differentiation: A Unified Theory of Differentiation Via New Derivate Theorems and New Derivatives / Edition 1

by Krishna M. Garg

Overview

Theory of differentiation includes all aspects of various kinds of derivates and derivatives, and the theory of various Perron and Denjoy-Perron integrals. Derivative theorems covered are theorems on unilateral (or Dini) derivates. Through a cohesive format, outstanding problems are resolved, new ones are presented, and developments in this field, both past and present, are covered.

Product Details

ISBN-13:	9780471253877
Publisher:	Wiley
Publication date:	09/23/1998
Series:	Wiley-Interscience and Canadian Mathematics Series of Monographs and Texts , #28
Pages:	544
Product dimensions:	6.46(w) x 9.41(h) x 1.20(d)

About the Author

Krishna M. Garg is the author of Theory of Differentiation: A Unified Theory of Differentiation Via New Derivate Theorems and New Derivatives, published by Wiley.

Table of Contents

A UNIFIED THEORY OF UNILATERIAL DERIVATES.

Definitions, Notations, and Preliminary Results.

Some Fundamental Theorems on Unilateral Derivates.

A THEORY OF SOME NEW DERIVATIVES.

Existence of New Derivatives.

Calculus of New Derivatives.

THEORY OF NEW DERIVATIVES (CONTINUED).

Monotonicity and Other Properties in Terms of New Derivatives.

Properties of New Derivatives and New Derivability Sets.

Denjoy and Perron Integrals Corresponding to New Derivatives.

SOME DIRECT APPLICATIONS OF THE THEORY OF NEW DERIVATIVES.

Derivates and Derivability of Symmetric, Quasismooth and Smooth Functions.

Strong Derivates and Strong Derivative.

UNIFIED AXIOMATIC THEORIES OF GENERALIZED DERIVATIVES.

A Unified Theory of Generalized Derivatives.

A Unified Theory of Generalized New Derivatives.

References.

Indexes.

Editorial Reviews

Presents a unified theory of unilateral derivates in terms of which every continuous function is derivable at a set of points which has cardinality c in every interval. Some of the new derivatives are also defined for real-valued functions on normed vector spaces. Contains sections on a unified theory of unilateral derivatives, a theory of some new derivatives, unified axiomatic theories of generalized derivatives, and unified theories of some other aspects of generalized derivatives. Annotation c. by Book News, Inc., Portland, Or.

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