Some properties of modified Szász-Mirakyan operators in polynomial spaces via the power summability method

• Autorzy: Braha Naim L.

Identyfikatory

DOI

https://doi.org/10.1515/jaa-2020-2006

• Języki publikacji: EN

Abstrakty

EN

In this paperwe will prove the Korovkin type theorem for modified Szász-Mirakyan operators via Astatistical convergence and the power summability method. Also we give the rate of the convergence related to the above summability methods, and in the last section, we give a kind of Voronovskaya type theorem for A-statistical convergence and Grüss-Voronovskaya type theorem.

Słowa kluczowe

EN

A-statistical convergence; modified Szasz-Mirakyan operator; power summability method; Korovkin type theorem; Voronovskaya type theorem; rate of convergence; Grüss-Voronovskaya type theorem

PL

konwergencja statystyczna; zmodyfikowane operatory Szasza-Mirakyana; metoda sumowania mocy; twierdzenie typu Korovkina; twierdzenie typu Woronowskiej; promień zbieżności; twierdzenie typu Grüssa-Woronowskiej

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2020
• Tom: Vol. 26, nr 1
• Strony: 79--90
• Opis fizyczny: Bibliogr. 22 poz.

Twórcy

autor

Braha Naim L.

• Department of Mathematics and Computer Sciences, University of Prishtina, Avenue Mother Teresa, No-5, Prishtina, 10000, Kosovo

Bibliografia

• [1] O. G. Atlihan, M. Unver and O. Duman, Korovkin theorems on weighted spaces: Revisited, Period. Math. Hungar. 75 (2017), no. 2, 201-209.
• [2] F. Başar, Summability Theory and its Applications, Bentham Science, Oak Park, 2012.
• [3] J. Boos, Classical and Modern Methods in Summability, Oxford Math. Monogr., Oxford University, Oxford, 2000.
• [4] N. L. Braha, Some weighted equi-statistical convergence and Korovkin type-theorem, Results Math. 70 (2016), no. 3-4, 433-446.
• [5] N. L. Braha, Some properties of Baskakov-Schurer-Szász operators via power summability methods, Quaest. Math. 42 (2019), no. 10, 1411-1426.
• [6] N. L. Braha, V. Loku and H. M. Srivastava, Λ2-weighted statistical convergence and Korovkin and Voronovskaya type theorems, Appl. Math. Comput. 266 (2015), 675-686.
• [7] N. L. Braha, H. M. Srivastava and S. A. Mohiuddine, 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 (2014), 162-169.
• [8] M. Campiti and G. Metafune, Lp-convergence of Bernstein-Kantorovich-type operators, Ann. Polon. Math. 63 (1996), no. 3, 273-280.
• [9] O. Duman, M. K. Khan and C. Orhan, A-statistical convergence of approximating operators, Math. Inequal. Appl. 6 (2003), no. 4, 689-699.
• [10] H. Fast, Sur la convergence statistique, Colloq. Math. 2 (1951), 241-244.
• [11] J. A. Fridy and H. I. Miller, A matrix characterization of statistical convergence, Analysis 11 (1991), no. 1, 59-66.
• [12] S. G. Gal and H. Gonska, Grüss and Grüss-Voronovskaya-type estimates for some Bernstein-type polynomials of real and complex variables, Jaen J. Approx. 7 (2015), no. 1, 97-122.
• [13] U. Kadak, N. L. Braha and H. M. Srivastava, Statistical weighted B-summability and its applications to approximation theorems, Appl. Math. Comput. 302 (2017), 80-96.
• [14] M. Kirisci and A. Karaisa, Fibonacci statistical convergence and Korovkin type approximation theorems, J. Inequal. Appl. 2017 (2017), Paper No. 229.
• [15] W. Kratz and U. Stadtmüller, Tauberian theorems for Jp-summability, J. Math. Anal. Appl. 139 (1989), no. 2, 362-371.
• [16] V. Loku and N. L. Braha, Some weighted statistical convergence and Korovkin type-theorem, J. Inequal. Spec. Funct. 8 (2017), no. 3, 139-150.
• [17] D. Soylemez and M. Unver, Korovkin type theorems for Cheney-Sharma operators via summability methods, Results Math. 72 (2017), no. 3, 1601-1612.
• [18] U. Stadtmüller and A. Tali, On certain families of generalized Nörlund methods and power series methods, J. Math. Anal. Appl. 238 (1999), no. 1, 44-66.
• [19] E. Taş, Some results concerning Mastroianni operators by power series method, Commun. Fac. Sci. Univ. Ank. Sér. A1 Math. Stat. 65 (2016), no. 1, 187-195.
• [20] E. Tas and T. Yurdakadim, Approximation by positive linear operators in modular spaces by power series method, Positivity 21 (2017), no. 4, 1293-1306.
• [21] M. Unver, Abel transforms of positive linear operators, AIP Conf. Proc. 1558 (2013), 1148-1151.
• [22] Z. Walczak, On certain positive linear operators in polynomial weight spaces, Acta Math. Hungar. 101 (2003), no. 3, 179-191.

Uwagi

Opracowanie rekordu ze środków MNiSW, umowa Nr 461252 w ramach programu "Społeczna odpowiedzialność nauki" - moduł: Popularyzacja nauki i promocja sportu (2020).