Convergence of Special Sequences of Semi-Exponential Operators

Abstract

Several papers, mainly written by J. de la Call and co-authors, contain modifications of classical sequences of positive linear operators to obtain new sequences converging to limits which are not necessarily the identity operator. Such results were obtained using probabilistic methods. Recently, results of this type have been obtained with analytic methods. Semi-exponential operators have also been introduced, extending the theory of exponential operators. We combine these two approaches, applying the semi-exponential operators in a new context and enlarging the list of operators representable as limits of other operators.

Construction of New Operators by Composition of Integral-Type Operators and Discrete Operators

“…Recently Gupta [10] obtained two new operators by combining exponential operator associated to 𝑥 3 with Szász-Mirakyan and Laguerre type operators.…”

Convergence estimates of semi-exponential operators associated with 1 + x 2

“…Varied authors examined approximation properties of these operators for functions from different function spaces (cf. [2], [5], [8], [10], [12] and [13]). Similar type of operators have been examined by numerous authors in the recent years (cf.…”

Approximation properties of a discrete operator

“…which is the Ismail-May exponential-type operator connected with the polynomial p(x) = x(1 + x) 2 (see [7, 3.14]).…”