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Journal of Applied Mathematics and Computing

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10.07.2020 | Original Research

Some weighted statistical convergence and associated Korovkin and Voronovskaya type theorems

verfasst von: Naim L. Braha, H. M. Srivastava, Mikail Et

Erschienen in: Journal of Applied Mathematics and Computing | Ausgabe 1-2/2021

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Abstract

In this paper, we propose to investigate a new weighted statistical convergence by applying the Nörlund–Cesáro summability method. Based upon this definition, we prove some properties of statistically convergent sequences and a kind of the Korovkin type theorems. We also study the rate of the convergence for this kind of weighted statistical convergence and a Voronovskaya type theorem.

Vorheriger Artikel A novel approach for the numerical approximation to the solution of singularly perturbed differential-difference equations with small shifts

Nächster Artikel An improved finite difference/finite element method for the fractional Rayleigh–Stokes problem with a nonlinear source term

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Altomare, F.: Korovkin-type theorems and approximation by positive linear operators. Surv. Approx. Theory 5, 92–164 (2010)MathSciNetMATH

Altın, Y., Et, M., Tripathy, B.C.: The sequence space \(|{\overline{N}}_{p}|(M, r, q, s)\) on seminormed spaces. Appl. Math. Comput. 154(2), 423–430 (2004)MathSciNetMATH

Altun, Y., Bilgin, T.: On a new class of sequences related to the \(l_{p}\) space defined by Orlicz function. Taiwan. J. Math. 13(4), 1189–1196 (2009)CrossRef

Bhardwaj, V.K., Singh, N.: Some sequence spaces defined by Orlicz functions. Demonstr. Math. 33(3), 571–582 (2000)MathSciNetMATH

Boyanov, B.D., Veselinov, V.M.: A note on the approximation of functions in an infinite interval by linear positive operators. Bull. Math. Soc. Sci. Math. R. S. Roumanie (N.S.) 14(62), 9–13 (1970). (1971)MathSciNetMATH

Braha, N.L., Mansour, T.: On \(\Lambda ^2\)-strong convergence of numerical sequences and Fourier series. Acta Math. Hungar. 141(1–2), 113–26 (2013)MathSciNetCrossRef

Braha, N.L.: A new class of sequences related to the \(l_{p}\) spaces defined by sequences of Orlicz functions. J. Inequal. Appl. 2011, Article ID 539745, 10 p (2011)

Braha, N.L.: Some properties of new modified Szász–Mirakyan operators in polynomial weight spaces via power summability method. Bull. Math. Anal. Appl. 10(3), 53–65 (2018)MathSciNetMATH

Braha, N.L.: Some properties of Baskakov–Schurer-Szász operators via power summability methods. Quaest. Math. 42(10), 1411–1426 (2019)MathSciNetCrossRef

10.

Braha Naim, L., Loku, V., Srivastava, H.M.: \(\Lambda ^{2} \)-weighted statistical convergence and Korovkin and Voronovskaya type theorems. Appl. Math. Comput. 266, 675–686 (2015)MathSciNetMATH

11.

Braha Naim, L., Srivastava, H.M., Mohiuddine, S.A.: A Korovkin’s type approximation theorem for periodic functions via the statistical summability of the generalized de la Vallée Poussin mean. Appl. Math. Comput. 228, 162–169 (2014)MathSciNetMATH

12.

Braha, N.L., Convergence, S.W.E.-S., Type-Theorem, K.: Some weighted equi-statistical convergence and Korovkin type-theorem. Results Math. 70(3–4), 433–446 (2016)MathSciNetCrossRef

13.

Braha, N.L., Et, M.: The sequence space \( E_n^q(M, p, s)\) and \(N_k\)-lacunary statistical convergence. Banach J. Math. Anal. 7(1), 88–96 (2013)MathSciNetCrossRef

14.

Braha, N.L.: Some geometric properties of \(N(\lambda, p)\)-spaces. J. Inequal. Appl. 112, 10 (2014)MathSciNetMATH

15.

Braha, Naim L.: On some properties of new paranormed sequence space defined by \(\lambda ^2\)-convergent sequences. J. Inequal. Appl. 273, 10 (2014)MathSciNetMATH

16.

Edely, O.H.H., Mohiuddine, S.A., Noman, A.K.: Korovkin type approximation theorems obtained through generalized statistical convergence. Appl. Math. Lett. 23, 1382–1387 (2010)MathSciNetCrossRef

17.

Et, M., Altin, Y., Choudhary, B., Tripathy, B.C.: On some classes of sequences defined by sequences of Orlicz functions. Math. Inequal. Appl. 9(2), 335–342 (2006)MathSciNetMATH

18.

Fast, H.: Sur la convergence statistique. Colloq. Math. 2, 241–244 (1951)MathSciNetCrossRef

19.

Kadak, U., Braha, N.L., Srivastava, H.M.: Statistical weighted \({B}\)-summability and its applications to approximation theorems. Appl. Math. Comput. 302, 80–96 (2017)MathSciNetMATH

20.

Korovkin, P.P.: Convergence of linear positive operators in the spaces of continuous functions (Russian). Doklady Akad. Nauk. SSSR (N.S.) 90, 961–964 (1953)MathSciNet

21.

Korovkin, P.P.: Linear Operators and Approximation Theory. Hindustan Publ. Co., Delhi (1960)

22.

Lindenstrauss, J., Tzafriri, L.: On Orlicz sequence spaces. Isr. J. Math. 1, 379–390 (1971)MathSciNetCrossRef

23.

Loku, V., Braha, N.L.: Some weighted statistical convergence and Korovkin type-theorem. J. Inequal. Spec. Funct. 8(3), 139–150 (2017)MathSciNet

24.

Mohiuddine, S.A., Alotaibi, A., Mursaleen, M.: Statistical summability \((C, 1)\) and a Korovkin type approximation theorem. J. Inequal. Appl. 2012, 172 (2012)MathSciNetCrossRef

25.

Mohiuddine, S.A., Alamri, B.A.S.: Generalization of equi-statistical convergence via weighted lacunary sequence with associated Korovkin and Voronovskaya type approximation theorems. Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM 113(3), 1955–1973 (2019)MathSciNetCrossRef

26.

Mursaleen, M., Alotaibi, A.: Statistical lacunary summability and a Korovkin type approximation theorem. Ann. Univ. Ferrara 57(2), 373–381 (2011)MathSciNetCrossRef

27.

Mursaleen, M., Karakaya, V., Erturk, M., Gursoy, F.: Weighted statistical convergence and its application to Korovkin type approximation theorem. Appl. Math. Comput. 218, 9132–9137 (2012)MathSciNetMATH

28.

Mursaleen, M., Khan, Q.A., Chishti, T.A.: Some new convergent sequences spaces defined by Orlicz functions and statistical convergence. Ital. J. Pure Appl. Math. 9, 25–32 (2001)MathSciNetMATH

29.

Srivastava, H.M., Mursaleen, M., Khan, A.: Generalized equi-statistical convergence of positive linear operators and associated approximation theorems. Math. Comput. Model. 55, 2040–2051 (2012)MathSciNetCrossRef

30.

Steinhaus, H.: Sur la convergence ordinaire et la convergence asymptotique. Colloq. Math. 2, 73–74 (1951)CrossRef

31.

Wang, J.-J., Xu, Z.-B.: Approximation with Jacobi weights by Baskakov operators. Taiwan. J. Math. 13(1), 157–168 (2009)MathSciNetCrossRef

Titel: Some weighted statistical convergence and associated Korovkin and Voronovskaya type theorems
verfasst von: Naim L. Braha
H. M. Srivastava
Mikail Et
Publikationsdatum: 10.07.2020
Verlag: Springer Berlin Heidelberg
Erschienen in: Journal of Applied Mathematics and Computing / Ausgabe 1-2/2021
Print ISSN: 1598-5865
Elektronische ISSN: 1865-2085
DOI: https://doi.org/10.1007/s12190-020-01398-5

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