Volume 4,  Issue 1, 2003

Article 12

THE ANALYTIC DOMAIN IN THE IMPLICIT FUNCTION THEOREM

H.C. CHANG, W. HE AND N. PRABHU

SCHOOL OF INDUSTRIAL ENGINEERING
PURDUE UNIVERSITY
WEST LAFAYETTE, IN 47907

E-Mail: prabhu@ecn.purdue.edu

Received 30 May, 2002; Accepted 12 September, 2002.
Communicated by: H.M. Srivastava

ABSTRACT.   The Implicit Function Theorem asserts that there exists a ball of nonzero radius within which one can express a certain subset of variables, in a system of analytic equations, as analytic functions of the remaining variables. We derive a nontrivial lower bound on the radius of such a ball. To the best of our knowledge, our result is the first bound on the domain of validity of the Implicit Function Theorem.
Key words:
Implicit Function Theorem, Analytic Functions.

2000 Mathematics Subject Classification:
30E10.

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Relatively B-Pseudomonotone Variational Inequalities Over Product of Sets
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Bounded Linear Operators in Probabilistic Normed Space
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Fundamental Inequalities on Firmly Stratified Sets and Some Applications
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Partitioned Cyclic Functional Equations
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Extensions of Popoviciu's Inequality Using a General Method
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The Analytic Domain in the Implicit Function Theorem
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Hadamard-type Inequalities for Quasiconvex Functions
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Iterative Schemes to Solve Nonconvex Variational Problems
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Second-order Differential Proximal Methods for Equilibrium Problems
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Some Integral Inequalities Related to Hilbert's
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Comments on Some Analytic Inequalities
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On Entire and Meromorphic Functions that Share Small Functions with their Derivatives
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Comparison of Green Functions for Generalized Schrödinger Operators on C1,1-Domains
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Erdős-Turán Type Inequalities
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Some Variants of Anderson's Inequality in C1-Classes
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