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Dergiler / Turkish Journal of Mathematics / 2002 / Cilt: 26 - Sayı: 2

On non-existence of Korovkin's theorem in the space of $L_p$-locally integrable functions

A. D. GADJIEV
E. İBİKLİ
Sayfa
207–214
Yayın Tarihi
2022-11-05
DOI
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It is shown that a Korovkin-type theorem does not hold in the weighted space of $L_p$-locally integrable functions on the whole real axis.

📌 3 Maddede Bu Makale

🎯
Amaç & Hipotez:It is shown that a Korovkin-type theorem does not hold in the weighted space of $L_p$-locally integrable functions on the whole real axis.
📊
Temel Bulgular & Veri:It is shown that a Korovkin-type theorem does not hold in the weighted space of $L_p$-locally integrable functions on the whole real axis.
💡
Sonuç & Katkı:It is shown that a Korovkin-type theorem does not hold in the weighted space of $L_p$-locally integrable functions on the whole real axis.
🔬Tür:Araştırma Makalesi
📍Kapsam:Genişletilmiş Akademik Örneklem
⚙️Değişkenler:Alan Parametreleri

Abstract

It is shown that a Korovkin-type theorem does not hold in the weighted space of $L_p$-locally integrable functions on the whole real axis.

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Bu Makaleye Atıf Yap

GADJIEV, A. D., İBİKLİ, E. (2022). On non-existence of Korovkin's theorem in the space of $L_p$-locally integrable functions. Turkish Journal of Mathematics, Cilt: 26 - Sayı: 2, 207–214. https://ajindex.com/articles/608871

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Kaynakça (1)

  1. P. P. Korovkin, Linear Operators and Approximations Theory, Delhi, Hindustan Press,1960 [2] F. Altomare, M. Campiti, Korovkin-type Approximation Theory and its applications, Walter de Gruyter, Berlin, New York, 1994. [3] A. D. Gadjiev, On P.P.Korovkin Type Theorems. Math. Zametki, Vol. 20, N5 (in Russian)(1976). [4] A. D. Gadziev, The convergence problem for a sequence of positive linear operators on unbounded sets, and Theorems analogous to that of P. P. Korovkin, Dokl.Akad. Nauk SSSR, Tom 218, N5. English Translated Soviet Math. Dokl. Vol.15, N5 (1974). [5] H. Berens, R. A. DeVore, Quantitative Korovkin theorems for positive linear operators in Lp space. Trans. Amer. Math. Soc., 245: 349-361 (1978). [6] K. Donner, Korovkin Theorems in Lp− spaces J. Functional Analysis 42 (1981), N1, p.12-28. [7] M. W. Müller, Lp− approximation by the method of integral Meyer-K¨onig and Zeller operators, Studia Math. 63 (1978), 81-88. [8] S. J. Bernau, Theorems of Korovkin type for Lp spaces, Paci c J. Math. 53 (1974), 11-19. [9] V. K. Dzyadik, On the approximation of functions by linear positive operators and singular integrals. Mat. Sbornik 70, 508-517, (in Russian) (1966). [10] W. Kitto and D. E. Wulbert, Korovkin approximations in Lp−spaces, Paci c J. Math. 63(1976), N1, 153-167.