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Iterates of q-Bernstein operators on triangular domain with all curved sides

Iliyas Mohammad, Khan Asif, Arif Mohd, Mursaleen Mohammad, Lone Mudassir Rashid

Demonstratio Mathematica

2022

Vol. 55, nr 1

891-899

In this article, Phillips-type Bernstein operators (Btm,qF)(t,s) and (Bsn,qF)(t,s) , their products, and Boolean sum based on q-integer have been studied on a triangle with all curved sides. Furthermore, convergence of iterates of these operators have been analyzed using the weakly Picard operators technique and the contraction principle.

Korovkin type theorem for sequences of operators depending on a parameter

Finta Z.

Demonstratio Mathematica

2015

Vol. 48, nr 3

391--403

We establish necessary and sufficient conditions for a parameter depending sequence (Ln,λ)n≥1 of positive linear operators such that (Ln,λ)n≥1 converges in the strong operator topology to its limit operator. Some applications of our theorem are also presented.