Dunkl generalization of Phillips operators and approximation in weighted spaces View Full Text


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Article Info

DATE

2020-07-17

AUTHORS

M. Mursaleen, Md. Nasiruzzaman, A. Kılıçman, S. H. Sapar

ABSTRACT

The purpose of this article is to introduce a modification of Phillips operators on the interval [12,∞)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$[ \frac{1}{2},\infty ) $\end{document} via a Dunkl generalization. We further define the Stancu type generalization of these operators as Sn,υ∗(f;x)=n2eυ(nχn(x))∑ℓ=0∞(nχn(x))ℓγυ(ℓ)∫0∞e−ntnℓ+2υθℓ−1tℓ+2υθℓγυ(ℓ)f(nt+αn+β)dt\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$\mathcal{S}_{n, \upsilon }^{\ast }(f;x)=\frac{n^{2}}{e_{\upsilon }(n\chi _{n}(x))}\sum_{\ell =0}^{\infty } \frac{(n\chi _{n}(x))^{\ell }}{\gamma _{\upsilon }(\ell )}\int _{0}^{\infty } \frac{e^{-nt}n^{\ell +2\upsilon \theta _{\ell }-1}t^{\ell +2\upsilon \theta _{\ell }}}{\gamma _{\upsilon }(\ell )}f ( \frac{nt+\alpha }{n+\beta } ) \,\mathrm{d}t$\end{document}, f∈Cζ(R+)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$f\in C_{\zeta }(R^{+})$\end{document}, and calculate their moments and central moments. We discuss the convergence results via Korovkin type and weighted Korovkin type theorems. Furthermore, we calculate the rate of convergence by means of the modulus of continuity, Lipschitz type maximal functions, Peetre’s K-functional and the second order modulus of continuity. More... »

PAGES

365

References to SciGraph publications

  • 2002-11. Approximation by modified Szasz—Mirakjan operators on weighted spaces in PROCEEDINGS - MATHEMATICAL SCIENCES
  • 2018-10-22. A Dunkl type generalization of Szász operators via post-quantum calculus in JOURNAL OF INEQUALITIES AND APPLICATIONS
  • 2015-09-17. Dunkl generalization of Szász operators via q-calculus in JOURNAL OF INEQUALITIES AND APPLICATIONS
  • 2019-09-09. Approximation by a generalized class of Dunkl type Szász operators based on post quantum calculus in JOURNAL OF INEQUALITIES AND APPLICATIONS
  • 2017-02-07. On modified Dunkl generalization of Szász operators via q-calculus in JOURNAL OF INEQUALITIES AND APPLICATIONS
  • 2016-12-31. Modified Stancu type Dunkl generalization of Szász–Kantorovich operators in REVISTA DE LA REAL ACADEMIA DE CIENCIAS EXACTAS, FÍSICAS Y NATURALES. SERIE A. MATEMÁTICAS
  • 2019-07-16. Dunkl-Gamma Type Operators Including Appell Polynomials in COMPLEX ANALYSIS AND OPERATOR THEORY
  • 2019-06-21. Approximation results on Dunkl generalization of Phillips operators via q-calculus in ADVANCES IN CONTINUOUS AND DISCRETE MODELS
  • 2018-11-22. A generalized Dunkl type modifications of Phillips operators in JOURNAL OF INEQUALITIES AND APPLICATIONS
  • 2018-10-04. A Chebyshev spectral method based on operational matrix for fractional differential equations involving non-singular Mittag-Leffler kernel in ADVANCES IN CONTINUOUS AND DISCRETE MODELS
  • 2017-02-23. Szász-Durrmeyer Operators Based on Dunkl Analogue in COMPLEX ANALYSIS AND OPERATOR THEORY
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