Displaying similar documents to “On an approximation processes in the space of analytical functions”

Korovkin-type theorems and applications

Nazim Mahmudov (2009)

Open Mathematics

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Let {T n} be a sequence of linear operators on C[0,1], satisfying that {T n (e i)} converge in C[0,1] (not necessarily to e i) for i = 0,1,2, where e i = t i. We prove Korovkin-type theorem and give quantitative results on C 2[0,1] and C[0,1] for such sequences. Furthermore, we define King’s type q-Bernstein operator and give quantitative results for the approximation properties of such operators.

Weaker convergence conditions for the secant method

Ioannis K. Argyros, Saïd Hilout (2014)

Applications of Mathematics

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We use tighter majorizing sequences than in earlier studies to provide a semilocal convergence analysis for the secant method. Our sufficient convergence conditions are also weaker. Numerical examples are provided where earlier conditions do not hold but for which the new conditions are satisfied.