Some Korovkin type approximation applications of power series methods

Uluçay H., ÜNVER M., Soylemez D.

REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS, vol.117, no.1, 2023 (SCI-Expanded, Scopus) identifier identifier

  • Publication Type: Article / Article
  • Volume: 117 Issue: 1
  • Publication Date: 2023
  • Doi Number: 10.1007/s13398-022-01360-z
  • Journal Name: REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS FISICAS Y NATURALES SERIE A-MATEMATICAS
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Aerospace Database, MathSciNet, zbMATH, DIALNET, Civil Engineering Abstracts
  • Keywords: Power series method, P-Statistical convergence, Integral summability, Korovkin type approximation theorem, POSITIVE LINEAR-OPERATORS, STATISTICAL CONVERGENCE, THEOREMS, SUMMABILITY, SEQUENCE, SPACES
  • Ankara University Affiliated: Yes

Abstract

Korovkin type approximation via summability methods is one of the recent interests of the mathematical analysis. In this paper, we prove some Korovkin type approximation theorems in L-q[a, b], the space of all measurable real valued qth power Lebesgue integrable functions defined on [a, b] for q >= 1, and C[a, b], the space of all continuous real valued functions defined on [a, b], via statistical convergence with respect to power series (summability) methods, integral summability methods and mu-statistical convergence of the power series transforms of positive linear operators. We also show with examples that the results obtained in the present paper are stronger than some existing approximation theorems in the literature.