We prove the following generalization of Cartwright–Littlewood fixed point theorem. Suppose h : R 2 → is an orientation preserving planar homeomorphism, and X acyclic continuum. Let C be a component ∩ ( ) . If there c ∈ such that O + ⊆ or − then also contains Our result generalizes earlier results Ostrovski Boroński, answers Question from Boroński (2017). The proof inspired by short Cartwright ...

In the present paper, measure differential equations involving the distributional Henstock-Kurzweil integral are investigated. Theorems on the existence and structure of the set of solutions are established by using Schauder$^prime s$ fixed point theorem and Vidossich theorem. Two examples of the main results paper are presented. The new results are generalizations of some previous results in t...

‎let ${x_{alpha}:alphainlambda}$ be a collection of topological spaces‎, ‎and $mathcal {g}_{alpha}$ be a grill on $x_{alpha}$ for each $alphainlambda$‎. ‎we consider tychonoffrq{}s type theorem for $x=prod_{alphainlambda}x_{alpha}$ via the above grills and a natural grill on $x$ ‎related to these grills, and present a simple proof to this theorem‎. ‎this immediately yields the classical theorem...