Local approximation properties of certain class of linear positive operators via I-convergence

Mehmet Özarslan; Hüseyin Aktuǧlu

Open Mathematics (2008)

  • Volume: 6, Issue: 2, page 281-286
  • ISSN: 2391-5455

Abstract

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In this study, we obtain a local approximation theorems for a certain family of positive linear operators via I-convergence by using the first and the second modulus of continuities and the elements of Lipschitz class functions. We also give an example to show that the classical Korovkin Theory does not work but the theory works in I-convergence sense.

How to cite

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Mehmet Özarslan, and Hüseyin Aktuǧlu. "Local approximation properties of certain class of linear positive operators via I-convergence." Open Mathematics 6.2 (2008): 281-286. <http://eudml.org/doc/269424>.

@article{MehmetÖzarslan2008,
abstract = {In this study, we obtain a local approximation theorems for a certain family of positive linear operators via I-convergence by using the first and the second modulus of continuities and the elements of Lipschitz class functions. We also give an example to show that the classical Korovkin Theory does not work but the theory works in I-convergence sense.},
author = {Mehmet Özarslan, Hüseyin Aktuǧlu},
journal = {Open Mathematics},
keywords = {A-statistical convergence; I-convergence; modulus of continuity; local smoothness},
language = {eng},
number = {2},
pages = {281-286},
title = {Local approximation properties of certain class of linear positive operators via I-convergence},
url = {http://eudml.org/doc/269424},
volume = {6},
year = {2008},
}

TY - JOUR
AU - Mehmet Özarslan
AU - Hüseyin Aktuǧlu
TI - Local approximation properties of certain class of linear positive operators via I-convergence
JO - Open Mathematics
PY - 2008
VL - 6
IS - 2
SP - 281
EP - 286
AB - In this study, we obtain a local approximation theorems for a certain family of positive linear operators via I-convergence by using the first and the second modulus of continuities and the elements of Lipschitz class functions. We also give an example to show that the classical Korovkin Theory does not work but the theory works in I-convergence sense.
LA - eng
KW - A-statistical convergence; I-convergence; modulus of continuity; local smoothness
UR - http://eudml.org/doc/269424
ER -

References

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  8. [8] Kolk E., The statistical convergence in Banach spaces, Acta Comment. Univ. Tartu. Math., 1991, 928, 41–52 
  9. [9] Kostyrko P., Mačaj M., Šalát T., I-convergence, Real Anal. Exchange, 2000, 26, 669–685 
  10. [10] Kostyrko P., Mačaj M., Šalát T., Sleziak M., I-convergence and I-limit points, Math. Slovaca, 2005, 55, 443–464 Zbl1113.40001
  11. [11] Miller H.I., A measure theoretical subsequence characterization of statistical convergence, Trans. Amer. Math. Soc., 1995, 347, 1811–1819 http://dx.doi.org/10.2307/2154976 Zbl0830.40002
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