Deferred weighted A-statistical convergence based upon the (p,q)-Lagrange polynomials and its applications to approximation theorems

• Autorzy: Srivastava H. M. , Jena B. B. , Paikray S. K. , Misra U. K.

Identyfikatory

DOI

10.1515/jaa-2018-0001

• Języki publikacji: EN

Abstrakty

EN

Recently, the notion of positive linear operators by means of basic (or q-) Lagrange polynomials and A-statistical convergence was introduced and studied in [M. Mursaleen, A. Khan, H. M. Srivastava and K. S. Nisar, Operators constructed by means of q-Lagrange polynomials and A-statistical approximation, Appl. Math. Comput. 219 2013, 12, 6911-6918]. In our present investigation, we introduce a certain deferred weighted A-statistical convergence in order to establish some Korovkin-type approximation theorems associated with the functions 1, t and t2 defined on a Banach space C[0,1] for a sequence of (presumably new) positive linear operators based upon (p,q)-Lagrange polynomials. Furthermore, we investigate the deferred weighted A-statistical rates for the same set of functions with the help of the modulus of continuity and the elements of the Lipschitz class. We also consider a number of interesting special cases and illustrative examples in support of our definitions and of the results which are presented in this paper.

Słowa kluczowe

EN

statistical convergence; Korovkin-type approximation theorems; rate of convergence; modulus of continuity; Lipschitz classes; Lagrange polynomial; Chan-Chyan-Srivastava polynomials

PL

konwergencja statystyczna; twierdzenie Korovkina; wskaźnik konwergencji; moduł ciągłości; klasa Lipschitza; wielomian Lagrange'a; wielomiany Chan-Chyan-Srivastavy

• Wydawca: De Gruyter
• Czasopismo: Journal of Applied Analysis
• Rocznik: 2018
• Tom: Vol. 24, nr 1
• Strony: 1--16
• Opis fizyczny: Bibliogr. 36 poz.

Twórcy

autor

Srivastava H. M.

• Department of Mathematics and Statistics, University of Victoria, Victoria, BC, V8W 3R4, Canada
• Department of Medical Research, China Medical University Hospital, China Medical University, Taichung 40402, Taiwan, P. R. China

autor

Jena B. B.

• Department of Mathematics, Veer Surendra Sai University of Technology, Burla 768018, Odisha, India

autor

Paikray S. K.

• Department of Mathematics, Veer Surendra Sai University of Technology, Burla 768018, Odisha, India

autor

Misra U. K.

• Department of Mathematics, National Institute of Science and Technology, Palur Hills, Golanthara 761008, Odisha, India

Bibliografia

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Uwagi

Opracowanie rekordu w ramach umowy 509/P-DUN/2018 ze środków MNiSW przeznaczonych na działalność upowszechniającą naukę (2018).