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We prove an implicit function theorem and an inverse function theorem for free noncommutative functions over operator spaces and on the set of nilpotent matrices. We apply these results to study dependence of the solution of the initial…

In this work the implicit function theorem is used for searching local symbolic resolution of differential equations. General results of existence for first order equations are proven and some examples, one relative to cavitation in a…

We study the systems of ordinary differential equations which are implicit with respect to the higher derivatives, appearing in the linear form, and their solutions near the singular points. The invertibility of the higher derivatives…

The Implicit and Inverse Function Theorems are special cases of a general Implicit/Inverse Function Theorem which can be easily derived from either theorem. The theorems can thus be easily deduced from each other via the generalized…

The central purpose of this article is to establish new inverse and implicit function theorems for differentiable maps with isolated critical points. One of the key ingredients is a discovery of the fact that differentiable maps with…

In the present paper we obtain a new homological version of the implicit function theorem and some versions of the Darboux theorem. Such results are proved for continuous maps on topological manifolds. As a consequence, some versions of…

We view a conic optimization problem that has a unique solution as a map from its data to its solution. If sufficient regularity conditions hold at a solution point, namely that the implicit function theorem applies to the normalized…

In this paper, we introduce a method of converting implicit equations to the usual forms of functions locally without differentiability. For a system of implicit equations which are equipped with continuous functions, if there are unique…

We prove implicit function theorems for mappings on topological vector spaces over valued fields. In the real and complex cases, we obtain implicit function theorems for mappings from arbitrary (not necessarily locally convex) topological…

In the context of the stream calculus, we present an Implicit Function Theorem (IFT) for polynomial systems, and discuss its relations with the classical IFT from calculus. In particular, we demonstrate the advantages of the stream IFT from…

In this paper, we prove common fixed point results for a self-mappings satisfying an implicit function which is general enough to cover a multitude of known as well as unknown contractions. Our results modify, unify, extend and generalize…

We introduce a notion of a noncommutative function defined on a domain of $d$-tuples of bounded operators on an infinite dimensional Hilbert space. Inverse and implicit function theorems in this setting are established. When these…

We study finite-dimensional nonassociative algebras. We prove the implicit function theorem for such algebras. This allows us to establish a correspondence between such algebras and quasigroups, in the spirit of classical correspondence…

The mixed problem for the implicit degenerating nonlinear parabolic equation is considered, and the solvability and behavior of solutions of this problem are studied. Furthermore, some classes of function spaces and their relations with…

We study the existence problem for a local implicit function determined by a system of nonlinear algebraic equations in the particular case when the determinant of its Jacobian matrix vanishes at the point under consideration. We present a…

We extend calculus from smooth manifolds to topological manifolds making use of a theory of generalized functions developed for this aim. Actually such extension fits into a boarder context: the universal construction of a site containing…

We present recent advances in the analysis of constrained optimization problems with constraints given by singular mappings obtained within the framework of the $p$-regularity theory developed over the last twenty years. In particular, we…

We introduce the notion of a regular quadratic equation and a regular NTQ system over a free group. We prove the results that can be described as Implicit function theorems for algebraic varieties corresponding to regular quadratic and NTQ…

In the paper, we improve our earlier results concerning the existence, uniqueness and differentiability of a global implicit function. Some application to a Cauchy problem for an integro-differential Volterra system of nonconvolution type,…

A system of singular integral equations with monotone and concave nonlinearity in the subcritical case is investigated. The specified system and its scalar analog have direct applications in various areas of physics and biology. In…