Korovkin-type approximation by operators in Riesz spaces via power series method

• Autorzy: Chil Elmiloud , Assili Marwa

Identyfikatory

DOI

10.1515/dema-2019-0041

• Języki publikacji: EN

Abstrakty

EN

In this paper we prove an Ozguç, Yurdakadim and Taş version of the Korovkin-type approximation by operators in the sense of the power series method. That is, we try to extend the Korovkin approximation theorems, obtained by Ozguç and Taş in 2016, and Taş and Yurdakadim in 2017, for concrete classes of Banach spaces to the class of Riesz spaces. Some applications are presented.

Słowa kluczowe

EN

Riesz space; uniform convergence; power series; power series method

PL

przestrzeń Riesza; zbieżność jednostajna; szereg potęgowy; metoda szeregów potęgowych

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2019
• Tom: Vol. 52, nr 1
• Strony: 490--495
• Opis fizyczny: Bibliogr. 16 poz.

Twórcy

autor

Chil Elmiloud

• University of Tunis, Institut préparatoire aux études d’ingenieurs de Tunis, 2 Rue jawaher lel Nehrou Monflery 1008, Tunisia

autor

Assili Marwa

• L.A.T.A.O. Faculty of sciences of Tunis University, ELManar Compus universitaire Elmanar, Tunisia

Bibliografia

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• [2] Wolff M., On the universal Korovkin closure of subsets in vector lattices, J. Approx. Theory, 1978, 22, 243-253
• [3] Altomare F., Korovkin-type and approximation by positive linear operators, Surv. Approx. Theory, 2010, 5, 92-164
• [4] Duman O., Orhan C., An abstract version of the Korovkin approximation theorem, Publ. Math. Debrecen, 2006, 69, 33-46
• [5] Guessab A., Schmeisser G., Two Korovkin-type theorems in multivariate approximation, Banach J. Math. Anal., 2008, 2, 221-128
• [6] Atlihan O. G., Tas E., An abstract version of the Korovkin theorem via A-summation process, Acta Math. Hungar., 2015, 145, 360-368
• [7] Wisniewska H., Wojtowicz M., Approximations of the Korovkin type in Banach lattices, Rev. R. Acad. Cienc. Exactas Fıs. Nat. Ser. A Mat. RACSAM, 2015, 109(1), 125-134
• [8] Dorai A., Chil E., Wojtowicz M., Korovkin-type approximation theory in Riesz spaces, Mediterr. J. Math., 2018, 15:169
• [9] Bardaro C., Boccuto A., Dimitriou X., Mantellini I., Abstract Korovkin-type theorems in modular spaces and applications, Cent. Eur. J. Math., 2013, 11(10), 1774-1784
• [10] Ozguc I., Tas E., A Korovkin-type approximation theorem and power series method, Results Math., 2016, 69(3-4), 497-504
• [11] Pinar O. S., Fadime D., A Korovkin-type theorem for double sequences of positive linear operators via power series method, Positivity, 2018, 22, 209-218
• [12] Yurdakadim T., Abstract Korovkin theory in modular spaces in the sense of power series method, Hacet. J. Math. Stat., 2018, 47(6), 1467-1477
• [13] Tas E., Yurdakadim T., Approximation by positive linear operators in modular spaces by power series method, Positivity, 2017, 21(4), 1293-1306
• [14] Aliprantis C. D, Burkinshaw O., Positive Operators, Academic Press, Orlando, 1985
• [15] Luxemburg W. A., Zaanen A. C., Riesz Spaces I, North-Holland, Amsterdam, 1971
• [16] Boos J., Classical and Modern Methods in Summability, Oxford Univ. Press. UK, 2000

Uwagi

PL

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2019).