27 citations · 95 across the 19 of their papers we have counts for
11 papers · 1 filter
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.
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.