Displaying similar documents to “Local approximation properties of certain class of linear positive operators via I-convergence”

I-convergence theorems for a class of k-positive linear operators

Mehmet Özarslan (2009)

Open Mathematics

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In this paper, we obtain some approximation theorems for k- positive linear operators defined on the space of analytical functions on the unit disc, via I-convergence. Some concluding remarks which includes A-statistical convergence are also given.

A Korovkin type approximation theorems via ℐ -convergence

Oktay Duman (2007)

Czechoslovak Mathematical Journal

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Using the concept of ℐ -convergence we provide a Korovkin type approximation theorem by means of positive linear operators defined on an appropriate weighted space given with any interval of the real line. We also study rates of convergence by means of the modulus of continuity and the elements of the Lipschitz class.

Lacunary equi-statistical convergence of positive linear operators

Hüseyin Aktuğlu, Halil Gezer (2009)

Open Mathematics

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In this paper, the concept of lacunary equi-statistical convergence is introduced and it is shown that lacunary equi-statistical convergence lies between lacunary statistical pointwise and lacunary statistical uniform convergence. Inclusion relations between equi-statistical and lacunary equi-statistical convergence are investigated and it is proved that, under some conditions, lacunary equi-statistical convergence and equi-statistical convergence are equivalent to each other. A Korovkin...

On integral type generalizations of positive linear operators

O. Duman, M. A. Özarslan, O. Doğru (2006)

Studia Mathematica

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We introduce a sequence of positive linear operators including many integral type generalizations of well known operators. Using the concept of statistical convergence we obtain some Korovkin type approximation theorems for those operators, and compute the rates of statistical convergence. Furthermore, we deal with the local approximation and the rth order generalization of our operators.

Remarks on statistical and I -convergence of series

Jaroslav Červeňanský, Tibor Šalát, Vladimír Toma (2005)

Mathematica Bohemica

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In this paper we investigate the relationship between the statistical (or generally I -convergence) of a series and the usual convergence of its subseries. We also give a counterexample which shows that Theorem 1 of the paper by B. C. Tripathy “On statistically convergent series”, Punjab. Univ. J. Math. 32 (1999), 1–8, is not correct.

Local convergence comparison between two novel sixth order methods for solving equations

Santhosh George, Ioannis K. Argyros (2019)

Annales Universitatis Paedagogicae Cracoviensis. Studia Mathematica

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The aim of this article is to provide the local convergence analysis of two novel competing sixth convergence order methods for solving equations involving Banach space valued operators. Earlier studies have used hypotheses reaching up to the sixth derivative but only the first derivative appears in these methods. These hypotheses limit the applicability of the methods. That is why we are motivated to present convergence analysis based only on the first derivative. Numerical examples...