arXiv subjects
Publications and source records attributed to Judit Makó.
The main goal of this paper is to prove a Hermite-Hadamard type inequality for certain Schur convex functions using, as one of the main tools in the proof, a Korovkin-type approximation theorem.
In this paper, the connection between the functional inequalities $$ f\Big(\frac{x+y}{2}\Big)\leq\frac{f(x)+f(y)}{2}+α_J(x-y) \qquad (x,y\in D)$$ and $$ \int_0^1f\big(tx+(1-t)y\big)ρ(t)dt \leqλf(x)+(1-λ)f(y) +α_H(x-y) \qquad (x,y\in D)$$ is investigated, where $D$ is a convex subset of a linear space, $f:D\to\R$, $α_H,α_J:D-D\to\R$ are even functions, $λ\in[0,1]$, and $ρ:[0,1]\to\R_+$ is an integrable nonnegative function with $\int_0^1ρ(t)dt=1$.
In this paper, strongly $(α,T)$-convex functions, i.e., functions $f:D\to \R$ satisfying the functional inequality $$ f(tx+(1-t)y)\leq tf(x)+(1-t)f(y)-tα\big((1-t)(x-y)\big)-(1-t)α\big(t(y-x)\big)$$ for $x,y\in D$ and $t\in T\cap[0,1]$ are investigated. Here $D$ is a convex set in a linear space, $α$ is a nonnegative function on $D-D$, and $T\subseteq\R$ is a nonempty set. The main results provide various characterizations of strong $(α,T)$-convexity in the case when $T$ is a subfield of $\R$.
In this paper, approximate lower and upper Hermite--Hadamard type inequalities are obtained for functions that are approximately convex with respect to a given Chebyshev system.
In this paper, approximate convexity and approximate midconvexity properties, called $φ$-convexity and $φ$-midconvexity, of real valued function are investigated. Various characterizations of $φ$-convex and $φ$-midconvex functions are obtained. Furthermore, the relationship between $φ$-midconvexity and $φ$-convexity is established.