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1

Some properties of modified Szász-Mirakyan operators in polynomial spaces via the power summability method

Braha Naim L.

Journal of Applied Analysis

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2020

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Vol. 26, nr 1

79--90

EN

In this paperwe will prove the Korovkin type theorem for modified Szász-Mirakyan operators via Astatistical convergence and the power summability method. Also we give the rate of the convergence related to the above summability methods, and in the last section, we give a kind of Voronovskaya type theorem for A-statistical convergence and Grüss-Voronovskaya type theorem.

2

Some triple difference rough Cesàro and lacunary statistical sequence spaces

Esi A., Subramanian N.

Journal of Mathematics and Applications

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2018

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Vol. 41

81--93

EN

We generalized the concepts in probability of rough Cesàro and lacunary statistical by introducing the difference operator Δ[αγ] of fractional order, where α is a proper fraction and γ = (γmnk) is any fixed sequence of nonzero real or complex numbers. We study some properties of this operator involving lacunary sequence θ and arbitrary sequence p = (prst) of strictly positive real numbers and investigate the topological structures of related with triple difference sequence spaces. The main focus of the present paper is to generalized rough Cesaro and lacunary statistical of triple difference sequence spaces and investigate their topological structures as well as some inclusion concerning the operator Δ[αγ].

3

Deferred weighted A-statistical convergence based upon the (p,q)-Lagrange polynomials and its applications to approximation theorems

Srivastava H. M., Jena B. B., Paikray S. K., Misra U. K.

Journal of Applied Analysis

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2018

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Vol. 24, nr 1

1--16

EN

Recently, the notion of positive linear operators by means of basic (or q-) Lagrange polynomials and A-statistical convergence was introduced and studied in [M. Mursaleen, A. Khan, H. M. Srivastava and K. S. Nisar, Operators constructed by means of q-Lagrange polynomials and A-statistical approximation, Appl. Math. Comput. 219 2013, 12, 6911-6918]. In our present investigation, we introduce a certain deferred weighted A-statistical convergence in order to establish some Korovkin-type approximation theorems associated with the functions 1, t and t2 defined on a Banach space C[0,1] for a sequence of (presumably new) positive linear operators based upon (p,q)-Lagrange polynomials. Furthermore, we investigate the deferred weighted A-statistical rates for the same set of functions with the help of the modulus of continuity and the elements of the Lipschitz class. We also consider a number of interesting special cases and illustrative examples in support of our definitions and of the results which are presented in this paper.

4

Rate of convergence of Szász-beta operators based on q-integers

Gupta P., Agrawal P. N.

Demonstratio Mathematica

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2017

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Vol. 50, nr 1

130--143

EN

The purpose of this paper is to establish the rate of convergence in terms of the weighted modulus of continuity and Lipschitz type maximal function for the q-Szász-beta operators. We also study the rate of A-statistical convergence. Lastly, we modify these operators using King type approach to obtain better approximation.

5

On generalized Baskakov-Durrmeyer-Stancu type operators

Kumar A. S., Finta Z., Agrawal P. N.

Demonstratio Mathematica

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2017

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Vol. 50, nr 1

144--155

EN

In this paper, we study some local approximation properties of generalized Baskakov-Durrmeyer-Stancu operators. First, we establish a recurrence relation for the central moments of these operators, then we obtain a local direct result in terms of the second order modulus of smoothness. Further, we study the rate of convergence in Lipschitz type space and the weighted approximation properties in terms of the modulus of continuity, respectively. Finally, we investigate the statistical approximation property of the new operators with the aid of a Korovkin type statistical approximation theorem.

6

On statistically lq-complete and c0s in measure convergences of sequences of measurable functions

Papanastasiou N., Papachristodoulos C., Dimitriou X.

Journal of Applied Analysis

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2016

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Vol. 22, nr 2

163--168

EN

We introduce and study s-lq-complete and c0s-μ convergences, and we obtain a new result regarding statistical convergences of sequences of measurable functions.