Iterates of a class of discrete linear operators via contraction principle. (English) Zbl 1096.41015

Agratini, Octavian; Rus, Ioan A.

Commentat. Math. Univ. Carol. 44, No. 3, 555-563 (2003).

Summary: In this paper we are concerned with a general class of positive linear operators of discrete type. Based on the results of the weakly Picard operator theory our aim is to study the convergence of the iterates of the defined operators and some approximation properties of our class as well. Some special cases in connection with binomial type operators are also revealed.

MSC:

41A36	Approximation by positive operators
47H10	Fixed-point theorems

Keywords:

linear positive operators; contraction principle; weakly Picard operators; delta operators; operators of binomial type