Feller's Scheme in Approximation by Nonlinear Possibilistic Integral Operators. (4th March 2017)

• Record Type: Journal Article
• Authors: Coroianu, Lucian; Gal, Sorin G.; Opris, Bogdan D.; Trifa, Sorin
• Is Part Of: Numerical functional analysis and optimization. Volume 38:Number 3(2017)
• Page Start: 327
• Page End: 343
• Publication Date: 2017-03-04
• Subjects: Nonlinear possibilistic integral -- possibilistic Gauss–Weierstrass operators -- possibilistic de la Vallée–Poussin operators -- possibilistic Fejér operators -- possibilistic Jackson operators -- possibilistic (max-product) Bernstein–kind operators -- possibilistic Picard operators -- possibilistic Poisson–Cauchy operators -- Theory of possibility, Feller's scheme; 41A36 -- 41A25 -- 28A10 -- 28E10 -- 28A25 -- 60E15; Functional analysis -- Periodicals; Numerical analysis -- Periodicals; Mathematical optimization -- Periodicals; Numerical Analysis, Computer-Assisted; 515.705
• DOI: 10.1080/01630563.2017.1279174
• Languages: English
• ISSNs: 0163-0563

Abstract

ABSTRACT: By analogy with Feller's general probabilistic scheme used in the construction of many classical convergent sequences of linear operators, in this paper, we consider a Feller-kind scheme based on the possibilistic integral, for the construction of convergent sequences of nonlinear operators. In particular, in the discrete case, all the so-called max-product Bernstein-type operators and their qualitative convergence properties are recovered. Also, discrete nonperiodic nonlinear possibilistic convergent operators of Picard type, Gauss–Weierstrass type and Poisson–Cauchy type are studied and the possibility of introduction of discrete periodic(trigonometric) nonlinear possibilistic operators of de la Vallée–Poussin type, of Fejér type and of Jackson type is mentioned as future directions of research.