Iryna Banakh

most citedOn Local Convexity Of Nonlinear Mappings Between Banach Spaces

2 citations · 2 across the 4 of their papers we have counts for

collaborators

4 papers

math.GR2023

Midconvex sets in Abelian groups

Iryna Banakh, Taras Banakh, Maria Kolinko +1

A subset $X$ of an Abelian group $G$ is called $mi d co n v e x$ if for every $x, y \in X$ the set $\frac{x + y}{2} = {z \in G : 2 z = x + y}$ is a subset of $X$ . We prove that a subset $X$ of an Abel…

math.MG2023

Metric characterizations of some subsets of the real line

Iryna Banakh, Taras Banakh, Maria Kolinko +1

A metric space $(X, d)$ is called a $s u b l in e$ if every 3-element subset $T$ of $X$ can be written as $T = {x, y, z}$ for some points $x, y, z$ such that $d (x, z) = d (x, y) + d (y, z)$ . By a cla…

math.GR2023

Semiaffine sets in Abelian groups

Iryna Banakh, Taras Banakh, Maria Kolinko +1

A subset $X$ of an Abelian group $G$ is called $se mia f f in e$ if for every $x, y, z \in X$ the set ${x + y - z, x - y + z}$ intersects $X$ . We prove that a subset $X$ of an Abelian group $G$ …

math.FA2012★ 2 cited

On Local Convexity Of Nonlinear Mappings Between Banach Spaces

Iryna Banakh, Taras Banakh, Anatolij Plichko +1

We find conditions for a smooth nonlinear map $f : U \to V$ between open subsets of Hilbert or Banach spaces to be locally convex in the sense that for some $c$ and each posit…