27 citations · 95 across the 19 of their papers we have counts for
22 papers
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…
A note on the Choquet type operators
Sorin G. Gal, Constantin P. Niculescu
In this note the Choquet type operators are introduced, in connection to Choquet's theory of integrability with respect to a not necessarily additive set function. Based on their p…
Approximation of Random Functions by Random Polynomials in the Framework of Choquet's Theory of Integration
Sorin G. Gal, Constantin Niculescu
Given a submodular capacity space, we prove the uniform convergence in capacity and also the uniform convergence in the Choquet-mean of order with a quantitative estimate,…
A Nonlinear Extension of Korovkin's Theorem
Sorin G. Gal, Constantin Niculescu
In this paper we extend the classical Korovkin theorems to the framework of comonotone additive, sublinear and monotone operators. Based on the theory of Choquet capacities, severa…
Kantorovich's Mass Transport Problem for Capacities
Sorin G. Gal, Constantin P. Niculescu
The aim of the present paper is to extend Kantorovich's mass transport problem to the framework of upper/lower continuous capacities and to prove the cyclic monotonicity of the sup…
The Abel-Steffensen inequality in higher dimensions
Constantin P. Niculescu
The Abel-Steffensen inequality is extended to the context of several variables. Applications to Fourier analysis of several variables and Riemann-Stieltjes integration are also inc…
A note on Abel's partial summation formula
Constantin P. Niculescu, Marius Marinel Stănescu
Several applications of Abel's partial summation formula to the convergence of series of positive vectors are presented. For example, when the norm of the ambient ordered Banach sp…
Relative Convexity and Its Applications
Constantin P. Niculescu, Ionel Roventa
We discuss a rather general condition under which the inequality of Jensen works for certain convex combinations of points not all in the domain of convexity of the function under…
New Jensen-type inequalities
Constantin P. Niculescu, Cătălin Irinel Spiridon
We develop a new framework for the Jensen-type inequalities that allows us to deal with functions not necessarily convex and Borel measures not necessarily positive.
Majorization in spaces with a curved geometry
Constantin P. Niculescu, Ionel Roventa
The Hardy-Littlewood-P?olya majorization theorem is extended to the framework of some spaces with a curved geometry (such as the global NPC spaces and the Wasserstein spaces). We a…
Some open problems concerning the convergence of positive series
Constantin P. Niculescu, Gabriel T. Prajitura
We discuss some old results due to Abel and Olivier concerning the convergence of positive series and prove a set of necessary conditions involving convergence in density.
Generalized convexity and the existence of finite time blow-up solutions for an evolutionary problem
Constantin P. Niculescu, Ionel Roventa
In this paper we study a class of nonlinearities for which a nonlocal parabolic equation with Neumann-Robin boundary conditions, for -Laplacian, has finite time blow-up solution…
An Extension of Young's Inequality
Flavia Corina Mitroi, Constantin P. Niculescu
Young's inequality is extended to the context of absolutely continuous measures. Several applications are included.