Approximation by Modified Meyer–König and Zeller Operators via Power Series Summability Method

2020 ◽  
Author(s):  
Naim L. Braha ◽  
Toufik Mansour ◽  
M. Mursaleen
Keyword(s):  
Power Series ◽  
Summability Method

scholarly journals Approximation by a power series summability method of Kantorovich type Szász operators including Sheffer polynomials

2021 ◽  
Vol 2021 (1) ◽  
Author(s):  
Valdete Loku ◽  
Naim L. Braha ◽  
Toufik Mansour ◽  
M. Mursaleen
Keyword(s):  
Power Series ◽  
Summability Method ◽  
Approximation Properties ◽  
Type Result ◽  
Szász Operators ◽  
Sheffer Polynomials

AbstractThe main purpose of this paper is to use a power series summability method to study some approximation properties of Kantorovich type Szász–Mirakyan operators including Sheffer polynomials. We also establish Voronovskaya type result.

XXII.—On Methods of Summability Based on Power Series

1957 ◽  
Vol 64 (4) ◽  
pp. 342-349
Author(s):  
D. Borwein
Keyword(s):  
Power Series ◽  
Summability Method ◽  
Radius Of Convergence ◽  
Main Concern ◽  
Image Position

SynopsisGiven a power series with real non-negative coefficients and having radius of convergence p, a summability method P is defined as follows:The main concern of this note is to establish conditions sufficient for one such method to include another.

scholarly journals A summability method due to linear differential equations and a uniqueness property of solutions of singular differential equations

1976 ◽  
Vol 20 (1) ◽  
pp. 41-51
Author(s):  
H. Gingold
Keyword(s):  
Power Series ◽  
Differential Equations ◽  
Formal Series ◽  
Summability Method ◽  
Linear Differential Equations ◽  
Uniqueness Property ◽  
Singular Differential Equations ◽  
Matching Process ◽  
Linear Differential ◽  
Natural Way

The purpose of this paper is to expose a method which will match a function f(z) existing in a domain D to a formal series whose radius of convergence may be zero. This matching process has to be done in a “natural way”, and has to be “regular”, which means that if a power series converges absolutely in the circle E = {z | |z|<r} then the summability function f(z) produced by our method in the domain D and matched to will coincide with in the domain E∩D. Euler, in his time, matched the function to the power series .

scholarly journals Some Properties of Kantorovich-Stancu-Type Generalization of Szász Operators including Brenke-Type Polynomials via Power Series Summability Method

2020 ◽  
Vol 2020 ◽  
pp. 1-15
Author(s):  
Naim Latif Braha ◽  
Toufik Mansour ◽  
Mohammad Mursaleen
Keyword(s):  
Power Series ◽  
Statistical Convergence ◽  
Type Theorem ◽  
Summability Method ◽  
Korovkin Type Theorem ◽  
Szász Operators

In this paper, we study the Kantorovich-Stancu-type generalization of Szász-Mirakyan operators including Brenke-type polynomials and prove a Korovkin-type theorem via the T-statistical convergence and power series summability method. Moreover, we determine the rate of the convergence. Furthermore, we establish the Voronovskaya- and Grüss-Voronovskaya-type theorems for T-statistical convergence.

The Software «MMI–calibration 3.0»

Metrologiya ◽  
2020 ◽  
pp. 16-24
Author(s):  
Alexandr D. Chikmarev
Keyword(s):  
Power Series ◽  
Data Processing ◽  
Statistical Treatment ◽  
Correction Function ◽  
Calibration Function ◽  
Measuring Instrument ◽  
Working Standard ◽  
Calibration Protocol ◽  
Error Probabilities ◽  
Continuous Power

A single program has been developed to ensure that the final result of the data processing of the measurement calibration protocol is obtained under normal conditions. The calibration result contains a calibration function or a correction function in the form of a continuous sedate series and a calibration chart based on typical additive error probabilities. Solved the problem of the statistical treatment of the calibration protocol measuring in normal conditions within a single program “MMI–calibration 3.0” that includes identification of the calibration function in a continuous power series of indications of a measuring instrument and chart calibration. An example of solving the problem of calibration of the thermometer by the working standard of the 3rd grade with the help of the “MMI-calibration 3.0” program.

Classical Tauberian Theorems for the (C; 1; 1) Summability Method

2014 ◽  
Vol 0 (0) ◽  
Author(s):  
Ümit Totur
Keyword(s):  
Tauberian Theorem ◽  
Summability Method ◽  
Subject Classification ◽  
Tauberian Theorems ◽  
Double Sequences ◽  
Littlewood Theorem

Abstract In this paper we generalize some classical Tauberian theorems for single sequences to double sequences. One-sided Tauberian theorem and generalized Littlewood theorem for (C; 1; 1) summability method are given as corollaries of the main results. Mathematics Subject Classification 2010: 40E05, 40G0

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