A Note on Global Implicit Function Theorem
نویسندگان
چکیده
We study the boundary behaviour of some certain maximal implicit function. We give estimates of the maximal balls on which some implicit functions are defined and we consider some cases when the implicit function is globally defined. We extend in this way an earlier result from [3] concerning an inequality satisfied by the partial derivatives ∂h ∂x and ∂h ∂y of the map h which verifies the global implicit function problem h (t, x) = h (a, b) , x (a) = b.
منابع مشابه
A Note on the Descent Property Theorem for the Hybrid Conjugate Gradient Algorithm CCOMB Proposed by Andrei
In [1] (Hybrid Conjugate Gradient Algorithm for Unconstrained Optimization J. Optimization. Theory Appl. 141 (2009) 249 - 264), an efficient hybrid conjugate gradient algorithm, the CCOMB algorithm is proposed for solving unconstrained optimization problems. However, the proof of Theorem 2.1 in [1] is incorrect due to an erroneous inequality which used to indicate the descent property for the s...
متن کاملSTRONGLY REGULAR NONSMOOTH GENERALIZED EQUATIONS (revised)
This note presents an implicit function theorem for generalized equations, simultaneously generalizing Robinson’s implicit function theorem for strongly regular generalized equations and Clarke’s implicit function theorem for equations with Lipschitz-continuous mappings.
متن کاملA generalized implicit enumeration algorithm for a class of integer nonlinear programming problems
Presented here is a generalization of the implicit enumeration algorithm that can be applied when the objec-tive function is being maximized and can be rewritten as the difference of two non-decreasing functions. Also developed is a computational algorithm, named linear speedup, to use whatever explicit linear constraints are present to speedup the search for a solution. The method is easy to u...
متن کامل$S$-metric and fixed point theorem
In this paper, we prove a general fixed point theorem in $textrm{S}$-metric spaces for maps satisfying an implicit relation on complete metric spaces. As applications, we get many analogues of fixed point theorems in metric spaces for $textrm{S}$-metric spaces.
متن کاملA note on spectral mapping theorem
This paper aims to present the well-known spectral mapping theorem for multi-variable functions.
متن کامل