Properties and characterizations of convex functions on time scales
Journal Title: Annales Mathematicae Silesianae - Year 2018, Vol 32, Issue
Abstract
In this research we deal with algebraic properties and characterizations of convex functions in the context of a time scale; this notion of convexity has been studied for some other authors but the setting of properties are establish here. Moreover, characterizations, a separation theorem and an inequality of Jensen type for this class of functions are shown as well.
Authors and Affiliations
Teodoro Lara, Nelson Merentes, Edgar Rosales, Ambrosio Tineo
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The abstract Cauchy problem on scales of Banach space was considered by many authors. The goal of this paper is to show that the choice of the space on scale is significant. We prove a theorem that the selection of the s...
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We provide an entropy estimate from below for a finitely generated group of transformation of a compact metric space which contains a ping-pong game with several players located anywhere in the group.
Mixed type of additive and quintic functional equations
In this paper, we investigate the general solution and Hyers–Ulam–Rassias stability of a new mixed type of additive and quintic functional equation of the form $$f(3x + y) - 5f(2x + y) + f(2x - y) + 10f(x + y) - 5f(x - y...
Solutions and stability of generalized Kannappan’s and Van Vleck’s functional equations
We study the solutions of the integral Kannappan’s and Van Vleck’s functional equations $$∫_{S}f(xyt)dμ(t) +∫_{S}f(xσ(y)t)dμ(t) = 2f(x)f(y), x,y∈S;$$ $$∫_{S}f(xσ(y)t)dμ(t)−∫_{S}f(xyt)dμ(t) = 2f(x)f(y), x,y∈S,$$ where $...