27 citations · 95 across the 19 of their papers we have counts for
10 papers · 1 filter
Old and new on the 3-convex functions
Dan-Ştefan Marinescu, Constantin P. Niculescu
The present paper aims to survey known results and to point out the wealth of rather important open problems that are out there.
Nonlinear operator extensions of Korovkin's theorems
Sorin G. Gal, Constantin P. Niculescu
In this paper we extend Korovkin's theorem to the context of sequences of weakly nonlinear and monotone operators defined on certain Banach function spaces. Several examples illust…
Quantitative estimates of convergence in nonlinear operator extensions of Korovkin's theorems
Sorin G. Gal, Constantin P. Niculescu
This paper is aimed to prove a quantitative estimate (in terms of the modulus of continuity) for the convergence in the nonlinear version of Korovkin's theorem for sequences of wea…
The Hornich-Hlawka functional inequality for functions with positive differences
Constantin P. Niculescu, Suvrit Sra
We analyze the role played by -convexity for the fulfillment of a series of linear functional inequalities that extend the Hornich-Hlawka functional inequality, $f\left( x\right…
Quantitative Korovkin theorems for sublinear, monotone and strongly translatable operators in
Sorin G. Gal, Constantin P. Niculescu
By extending the classical quantitative approximation results for positive and linear operators in of Berens and DeVore in 1978 and of Swetits a…
Korovkin type theorems for weakly nonlinear and monotone operators
Sorin G. Gal, Constantin P. Niculescu
In this paper we prove analogues of Korovkin's theorem in the context of weakly nonlinear and monotone operators acting on Banach lattices of functions of several variables. Our re…
A new look at the Hardy-Littlewood-Pólya inequality of majorization
Constantin P. Niculescu
The Hardy-Littlewood-Pólya inequality of majorization is extended to the framework of ordered Banach spaces. Several applications illustrating our main results are also included.
Nonlinear versions of Korovkin's abstract theorems
Sorin G. Gal, Constantin P. Niculescu
In this paper we prove Korovkin type theorems for sequences of sublinear, monotone and weak additive operators acting on function spaces C(X); where X is a compact or a locally com…
Choquet operators associated to vector capacities
Sorin G. Gal, Constantin P. Niculescu
The integral representation of Choquet operators defined on a space C(X) is established by using the Choquet-Bochner integral of a real-valued function with respect to a vector cap…
A note on the isotonic vector-valued convex functions
Constantin P. Niculescu, Octav Olteanu
The property of isotonicity of a continuous convex function defined on the entire space or only on the positive cone is characterized via subdifferentials. Numerous examples illust…