Approximation Results For q-Szãsz Mirakjan type operators | ||
| Journal of College of Education for Pure Science | ||
| Article 1, Volume 4, Issue 2, December 2014, Pages 1-12 | ||
| Author | ||
| Hasan Ali Naser | ||
| Abstract | ||
| In this paper, we introduce and study a new type q-Szãsz Mirakjan operators L_n (f,q_n;x) based on the q-integers in the case q_n∈(0,1), where q_n→1 as n→∞. First, we prove that these operators are converging to the function being approximated. Then, we define the m-th order q-moments and find a recurrence relation for these q-moments. Finally, we prove Voronovskaja-type asymptotic formulas for the operators L_n (f,q_n;x). | ||
| Keywords | ||
| integers; sz Mirakjann operators; linear positive operators; sequence of positive numbers; Voronovskaja; type asymptotic formulas | ||
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