On One Theorem of S. Warschawski

On Differentiability at the Boundary in Conformal Mapping1

Introduction. The object of this note is to present a short and simple proof of the following two theorems. Theorem 1. Suppose that C is a closed rectifiable Jordan curve in the complex l-plane and that C has a continuously turning tangent in a neighborhood of one of its points, XoSuppose, furthermore, that the tangent angle t(s) as function of the arc length s has a modulus of continuity (¡)(t...

On Conformal Mapping of Nearly Circular Regions

On injectivity of a class of monotone operators with some univalency consequences

In this paper we provide sufficient conditions that ensure the convexity of the inverse images of an operator, monotone in some sense. Further, conditions that ensure the monotonicity, respectively the local injectivity of an operator are also obtained. Combining the conditions that provide the local injectivity, respectively the convexity of the inverse images of an operator, we are able to ob...

$S$-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.

On a class of systems of n Neumann two-point boundary value Sturm-Liouville type equations

Employing a three critical points theorem, we prove the existence ofmultiple solutions for a class of Neumann two-point boundary valueSturm-Liouville type equations. Using a local minimum theorem fordifferentiable functionals the existence of at least one non-trivialsolution is also ensured.