scholarly journals On statistical and strong convergence with respect to a modulus function and a power series method

Filomat ◽  
2020 ◽  
Vol 34 (12) ◽  
pp. 3981-3993
Author(s):  
Cemal Belen ◽  
Mustafa Yıldırım ◽  
Canan Sümbül
Keyword(s):  
Power Series ◽  
Strong Convergence ◽  
Statistical Convergence ◽  
Modulus Function ◽  
Series Method ◽  
Power Series Method

This paper introduces and focuses on two pairs of concepts in two main sections. The first section aims to examine the relation between the concepts of strong Jp-convergence with respect to a modulus function f and Jp-statistical convergence, where Jp is a power series method. The second section introduces the notions of f-Jp-statistical convergence and f -strong Jp-convergence and discusses some possible relations among them.

scholarly journals A Link between Approximation Theory and Summability Methods via Four-Dimensional Infinite Matrices

Mathematics ◽  
2021 ◽  
Vol 9 (16) ◽  
pp. 1895
Author(s):  
Hari M. Srivastava ◽  
Khursheed J. Ansari ◽  
Faruk Özger ◽  
Zeynep Ödemiş Özger
Keyword(s):  
Computer Graphics ◽  
Power Series ◽  
Approximation Theory ◽  
Statistical Convergence ◽  
Series Method ◽  
Power Series Method ◽  
Summability Methods ◽  
Korovkin Type Theorems ◽  
Convergence Type ◽  
Theoretical Results

In this study, we present a link between approximation theory and summability methods by constructing bivariate Bernstein-Kantorovich type operators on an extended domain with reparametrized knots. We use a statistical convergence type and power series method to obtain certain Korovkin type theorems, and we study certain rates of convergences related to these summability methods. Furthermore, we numerically analyze the theoretical results and provide some computer graphics to emphasize the importance of this study.

scholarly journals A theory of variations via P-statistical convergence

2021 ◽  
Vol 110 (124) ◽  
pp. 11-27
Author(s):  
Kamil Demirci ◽  
Dragan Djurcic ◽  
Ljubisa Kocinac ◽  
Sevda Yıldız
Keyword(s):  
Power Series ◽  
Statistical Convergence ◽  
Series Method ◽  
Power Series Method ◽  
Limit Value ◽  
Statistical Variations

We introduce some notions of variation using the statistical convergence with respect to power series method. By the use of the notions of variation, we prove criterions that can be used to verify convergence without using limit value. Also, some results that give relations between P-statistical variations are studied.

The Scope of the Power Series Method

2013 ◽  
Vol 86 (1) ◽  
pp. 56-62
Author(s):  
Richard Beals
Keyword(s):  
Power Series ◽  
Series Method ◽  
Power Series Method
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