Year: 2025
Type: article
Abstract: In the present paper we consider $$\omega $$ -convex functions which generalized many well-known and intensively investigated classes of functions. Among other results, we prove the Jensen inequality for $$\omega $$ -convex functions, we examine operations preserving the $$\omega $$ -convexity and give several sufficient conditions which guarantee the continuity of such functions. The main result of the paper is a counterpart of a celebrated Hahn-Banach theorem for $$\omega $$ -convex functions. Several consequences are also contained in the paper.
Source: Results in Mathematics
Author: Andrzej Olbryś
Institution: University of Silesia in Katowice
Language: English
Subfield: Applied Mathematics
Field: Mathematics
Domain: Physical Sciences
Open Access status: hybrid
Estimated APC paid: $3,090
OpenAlex ID: W4410385803