<mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>q</mml:mi></mml:math>-Cesáro matrix and <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" altimg="si1.gif" display="inline" overflow="scroll"><mml:mi>q</mml:mi></mml:math>-statistical convergence

Journal of Function Spaces

2022

“…Defining a q-analog of the Cesàro matrix C 1 is not unique (see [15,16]). Here, we consider the q-Cesàro matrix, C 1 ðqÞ = ðc 1 nk ðq k ÞÞ ∞ n,k=0 , defined by…”

Section: Q-statistical Convergencementioning

confidence: 99%

“…Recently, Aktuğlu and Bekar [16] defined q-density and q-statistical convergence. The q-density is defined by…”

Section: Q-statistical Convergencementioning

confidence: 99%

See 1 more Smart Citation

Approximation Properties and $q$ -Statistical Convergence of Stancu-Type Generalized Baskakov-Szász Operators

Cai

Kılıçman

Journal of Function Spaces

2022

“…Recently, Aktu glu and Bekar [3] studied the notion of density and statistical convergence via q-calculus. Let E be subset of the set of natural numbers N. Then…”

Section: Approximation Via Q-statistical Convergencementioning

confidence: 99%

“…defines the q-density, where C 1 (q) = (c 1 nk (q k )) ∞ n,k=0 is the q-Cesàro matrix (see [1], [3]) defined by…”

Section: Approximation Via Q-statistical Convergencementioning

confidence: 99%

Szász type operators involving Charlier polynomials and approximation properties

Al-Abied

2021

Filomat

Our aim is to define modified Sz?sz type operators involving Charlier polynomials and obtain some approximation properties. We prove some results on the order of convergence by using the modulus of smoothness and Peetre?s K-functional. We also establish Voronoskaja type theorem for these operators. Moreover, we prove a Korovkin type approximation theorem via q-statistical convergence.

Uniform convergence of Fourier series via deferred Cesàro mean and its applications

Jena

Paikray

Math Methods in App Sciences

2022

In this article, we found an undesirable feature in the theory of summability; that is, the Fourier series of 2π$$ 2\pi $$‐periodic functions is uniformly convergent to the functions via the Ceàsro mean. However, it does not preserve the uniform convergence for the arbitrary periodic functions. To overcome this limitation, the objective of the paper is to introduce and study the notion of deferred Ceàsro mean based on the q$$ q $$ integers for the Fourier series of arbitrary periodic functions. We further study the behavior of our proposed method under both ordinary and statistical versions of convergence and accordingly establish two Korovkin‐type approximation theorems for trigonometric test functions. Finally, we also provide some examples with geometrical illustrations in support of the effectiveness of our results established in this work.