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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 operators 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(More)
The paper centers around a pair of sequences of linear positive operators. The former has the degree of exactness one and the latter has its degree of exactness null, but, as a novelty, it reproduces the third test function of Korovkin theorem. Quantitative estimates of the rate of convergence are given in different function spaces traveling from classical(More)
Let X be a Banach space, where exists a total sequence of mutually orthogonal continuous projections (T k) on X. Then with each x ∈ X we can associate its formal Fourier expansion x ∼ k T k x. Let Z r (r > 0) be the Zygmund method, M ϕ = (ϕ(k/(n + 1))) the triangular summa-tion method, defined by the differentiable function ϕ and Z r n x, M ϕ n x be Z r-and(More)
The topic of the present paper are certain approximation operators acting on the space of continous functions on [0,+∞) having polynomial growth. The operators which were defined by Jain in 1972 are based on a probability distribution which is called generalized Poisson distribution. As a main result we derive a complete asymptotic expansion for the(More)
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