Dmitri Goloubentsev, Evgeny Lakshtanov and Vladimir Piterbarg explain in mathematical terms, and demonstrate using a simple example, how the automatic implicit function theorem, a special version of ...
The paper presents a variant of implicit function theorem, as a corollary of existence theorem for solutions of a first order system of partial differential equations. This results is then extend to ...
ABSTRACT: In this paper, the well known implicit function theorem was applied to study existence and uniqueness of periodic solution of Duffing-type equation. Un-der appropriate conditions around the ...
Abstract: In this note, we discuss a generalization of the well-known implicit function theorem to the time-delay case. We show that the latter problem is closely related to the bicausal changes of ...
We combine a "global" version of the classical inverse function theorem with Schauder's fixed point theorem to investigate the existence and continuity properties of a function $(F, x) \rightarrow ...
ABSTRACT: In this paper, the well known implicit function theorem was applied to study existence and uniqueness of periodic solution of Duffing-type equation. Un-der appropriate conditions around the ...
This research paper explores the extension of the Implicit Function Theorem (IFT) to fractal sets. The objective is to establish the existence and differentiability of implicitly defined functions on ...
Automatic differentiation is a transformation of the computational graph associated with the algorithmic implementation of a mathematical function. It breaks it down into atomistic primitive ...
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