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A sharpened form of the inverse function theorem

100%

Elin M., Shoikhet D.

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

2019

tom 73

nr 2

In this note we establish an advanced version of the inverse function theorem and study some local geometrical properties like starlikeness and hyperbolic convexity of the inverse function under natural restrictions on the numerical range of the underlying mapping.

Coefficient body for nonlinear resolvents

100%

Elin M., Jacobzon F.

Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

2019

tom 73

nr 2

This paper is devoted to the study of families of so-called nonlinear resolvents. Namely, we construct polynomial transformations which map the closed unit polydisks onto the coefficient bodies for the resolvent families. As immediate applications of our results we present a covering theorem and a sharp estimate for the Schwarzian derivative at zero on the class of resolvents.

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2 Annales Universitatis Mariae Curie-Skłodowska, sectio A – Mathematica

2 Elin M.

1 Jacobzon F.

1 Shoikhet D.

2 2019

Wyniki wyszukiwania

A sharpened form of the inverse function theorem

Coefficient body for nonlinear resolvents