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8 papers · 2 filters
Convexity and a Stone-type theorem for convex sets in abelian semigroup setting
Witold Jarczyk, Zsolt Páles
In this paper, two parallel notions of convexity of sets are introduced in the abelian semigroup setting. The connection of these notions to algebraic and to set-theoretic operatio…
Convexity with respect to families of means
Gyula Maksa, Zsolt Páles
In this paper we investigate continuity properties of functions that satisfy the -Jensen convexity inequality $$ f\big(H_p(x,y)\big)\leq H_q(…
Characterization of the Hardy property of means and the best Hardy constants
Zsolt Páles, Paweł Pasteczka
The aim of this paper is to characterize in broad classes of means the so-called Hardy means, i.e., those means that sat…
Bernstein--Doetsch type theorems with Tabor type error terms for set-valued maps
Attila Gilányi, Carlos Gonzales, Kazimierz Nikodem +1
In this paper, we investigate set-valued maps of strongly and approximately Jensen convex and Jensen concave type. We present counterparts of the Bernstein--Doetsch Theorem with Ta…
Implications between generalized convexity properties of real functions
Tibor Kiss, Zsolt Páles
Motivated by the well-known implications among -convexity properties of real functions, analogous relations among the upper and lower -convexity properties of real functions…
Characterizations of higher-order convexity properties with respect to Chebyshev systems
Zsolt Páles, Éva Székelyné Radácsi
In this paper various notions of convexity of real functions with respect to Chebyshev systems defined over arbitrary subsets of the real line are introduced. As an auxiliary notio…