• Media type: E-Article
  • Title: Korovkin Type Approximation Theorems via Lacunary Equistatistical Convergence
  • Contributor: Alotaibi, Abdullah; Mursaleen, M.
  • Published: Faculty of Sciences and Mathematics, University of Niš, 2016
  • Published in: Filomat, 30 (2016) 13, Seite 3641-3647
  • Language: English
  • ISSN: 0354-5180; 2406-0933
  • Origination:
  • Footnote:
  • Description: <label>Abstract.</label> <p>H. Aktuğlu and H. Gezer [Central European J. Math. 7 (2009), 558–567] introduced the concepts of lacunary equistatistical convergence, lacunary statistical pointwise convergence and lacunary statistical uniform convergence for sequences of functions. In this paper, we apply the notion of lacunary equistatistical convergence to prove a Korovkin type approximation theorem by using test functions 1,<inline-formula> <mml:math display="inline"> <mml:mrow> <mml:mfrac> <mml:mi>x</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>−</mml:mo> <mml:mi>x</mml:mi> </mml:mrow> </mml:mfrac> <mml:mo>,</mml:mo> <mml:msup> <mml:mrow> <mml:mrow> <mml:mo>(</mml:mo> <mml:mrow> <mml:mfrac> <mml:mi>x</mml:mi> <mml:mrow> <mml:mn>1</mml:mn> <mml:mo>−</mml:mo> <mml:mi>x</mml:mi> </mml:mrow> </mml:mfrac> </mml:mrow> <mml:mo>)</mml:mo> </mml:mrow> </mml:mrow> <mml:mn>2</mml:mn> </mml:msup> </mml:mrow> </mml:math> </inline-formula>.</p>
  • Access State: Open Access