A new weighted statistical convergence and some associated approximation theorems

Braha, Naim L.; Loku, Valdete; Mansour, Toufik; Mursaleen, M.

doi:10.1002/mma.8134

Cited by 4 publications

(4 citation statements)

References 24 publications

(23 reference statements)

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“…P in 2021, see [29] for more information. Thus, in this section, we introduce the weighted (E λ , q)(C λ , 1) statistical convergence, which is a generalization of the weighted (E, 1)(C, 1), see [6] for more details.…”

Section: Weighted (E λ Q)(c λ 1) Statistical Convergencementioning

confidence: 99%

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Weighted (Eλ, q)(Cλ, 1) Statistical Convergence and Some Results Related to This Type of Convergence

et al. 2022

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In this paper, we defined weighted (Eλ,q)(Cλ,1) statistical convergence. We also proved some properties of this type of statistical convergence by applying (Eλ,q)(Cλ,1) summability method. Moreover, we used (Eλ,q)(Cλ,1) summability theorem to prove Korovkin’s type approximation theorem for functions on general and symmetric intervals. We also investigated some of the results of the rate of weighted (Eλ,q)(Cλ,1) statistical convergence and studied some sequences spaces defined by Orlicz functions.

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Section: Weighted (E λ Q)(c λ 1) Statistical Convergencementioning

confidence: 99%

“…We have referred to some of the papers that have different results related to statistical convergence, namely [3][4][5][6][7][8][9][10][11][12][13][14]. These results have contributed to developing the field of functional analysis and approximation theory.…”

Section: Introductionmentioning

confidence: 99%

Weighted (Eλ, q)(Cλ, 1) Statistical Convergence and Some Results Related to This Type of Convergence

et al. 2022

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“…The concept of statistical convergence of sequences in real numbers was introduced in 1951 by Fast in [12]. This concept has been studied under different names (see, [2,4,5,6,8,13,24,25,29,30,33,34,35]). Cone metric spaces were actually defined by several authors many years ago and took place under different names in the literature (see, for example [1,3,7,17,21,22,23]).…”

Section: Introductionmentioning

confidence: 99%

On Quasi I-Statistical Convergence of Triple Sequences in Cone Metric Spaces

2023

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Fast [12] is credited with pioneering the field of statistical convergence. This topic has been researched in many spaces such as topological spaces, cone metric spaces, and so on (see, for example [19, 21]). A cone metric space was proposed by Huang and Zhang [17]. The primary distinction between a cone metric and a metric is that a cone metric is valued in an ordered Banach space. Li et al. [21] investigated the definitions of statistical convergence and statistical boundedness of a sequence in a cone metric space. Recently, Sakaoğlu and Yurdakadim [29] have introduced the concepts of quasi-statistical convergence. The notion of quasi I-statistical convergence for triple and multiple index sequences in cone metric spaces on topological vector spaces is introduced in this study, and we also examine certain theorems connected to quasi I-statistically convergent multiple sequences. Finally, we will provide some findings based on these theorems.

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“…One of the main theorems in approximation theory is the Korovkin-type theorem. It is studied in various versions in various spaces; for more details, see [1,[14][15][16][17][18][19][20][21][22][23][24][25]. In what follows, we will give it for operators (1.2).…”

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confidence: 99%

Approximation properties by Bézier variant of the Baskakov–Schurer–Szász–Stancu operators

Braha,

Mansour,

Mursaleen

2023

Math Methods in App Sciences

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In this paper, we have construct a new version of the Bézier‐type Baskakov–Schurer–Szász–Stancu operators. For this new class of operators, uniform convergence is shown in any compact subset or positive real line. We prove Korovkin‐type theorem, Voronovskaya‐type theorem, and Grüss–Voronovskaya‐type theorem. Moreover, at the end, we express the behavior of the operators in the Lipschitz‐type space using the modulus of continuity and smoothness.

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A new weighted statistical convergence and some associated approximation theorems

Cited by 4 publications

References 24 publications

Weighted (Eλ, q)(Cλ, 1) Statistical Convergence and Some Results Related to This Type of Convergence

Weighted (Eλ, q)(Cλ, 1) Statistical Convergence and Some Results Related to This Type of Convergence

On Quasi I-Statistical Convergence of Triple Sequences in Cone Metric Spaces

Approximation properties by Bézier variant of the Baskakov–Schurer–Szász–Stancu operators

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