Zobrazeno 1 - 10
of 202
pro vyhledávání: '"Niculescu, Constantin P."'
In this survey, we review the many faces of the Hornich-Hlawka inequality. Several open problems that seem of utmost interest are mentioned.
Comment: 17 pages
Comment: 17 pages
Externí odkaz:
http://arxiv.org/abs/2407.03278
Autor:
Niculescu, Constantin P.
A quadrilateral inequality established by C. Sch\"otz in the context of Hilbert spaces is extended to the framework of Banach spaces. Our approach is based on the majorization theory and a substitute for the parallelogram law associated with Clarkson
Externí odkaz:
http://arxiv.org/abs/2405.20097
The present paper aims to survey known results and to point out the wealth of rather important open problems that are out there.
Comment: 20 pages
Comment: 20 pages
Externí odkaz:
http://arxiv.org/abs/2305.04353
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 illustrating the theory are included.
Comment: 17 pages
Comment: 17 pages
Externí odkaz:
http://arxiv.org/abs/2302.04786
Publikováno v:
Boll. delle Unione Mat. Ital., 2023
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 weakly nonlinear and monotone operators defined on spaces of continuous r
Externí odkaz:
http://arxiv.org/abs/2302.04779
Autor:
Niculescu, Constantin P., Sra, Suvrit
We analyze the role played by $n$-convexity for the fulfillment of a series of linear functional inequalities that extend the Hornich-Hlawka functional inequality, $f\left( x\right) +f\left( y\right) +f\left( z\right) +f\left( x+y+z\right) \geq f\lef
Externí odkaz:
http://arxiv.org/abs/2301.08342
By extending the classical quantitative approximation results for positive and linear operators in $L^{p}([0, 1]), 1\le p \le +\infty$ of Berens and DeVore in 1978 and of Swetits and Wood in 1983 to the more general case of sublinear, monotone and st
Externí odkaz:
http://arxiv.org/abs/2212.01262
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 results concern the convergence almost everywhere, the convergence in me
Externí odkaz:
http://arxiv.org/abs/2206.14102
Autor:
Niculescu, Constantin P.
Publikováno v:
J. Math. Anal. Appl. 501 (2021), Issue 2, paper 125211
The Hardy-Littlewood-P\'{o}lya inequality of majorization is extended to the framework of ordered Banach spaces. Several applications illustrating our main results are also included.
Comment: 18 pages
Comment: 18 pages
Externí odkaz:
http://arxiv.org/abs/2104.11605
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 compact metric space. Our results are illustrated by a series of examples
Externí odkaz:
http://arxiv.org/abs/2103.03661