Feller’s Scheme in Approximation by Nonlinear Possibilistic Integral Operators

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.

KEYWORDS:

• 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

2000 AMS MATHEMATICS SUBJECT CLASSIFICATION:

• 41A36
• 41A25
• 28A10
• 28E10
• 28A25
• 60E15