APPROXIMATION BY AN INTEGRAL TYPE APOSTOL-GENOCCHI OPERATORS
DOI:
https://doi.org/10.5281/4j96aa68Abstract
The goal of the current paper is to present an integral type FavardSzasz operators including Apostol-Genocchi poynomials. With the help of
the moments, we investigate the order of convergence in terms of the first
and the second order modulus of continuity and Peetres K-functional. We
also examine the convergence in the weighted spaces of functions by means of
weighted Korovkin type theorem.
References
[1] Q. Cai, B. C¸ ekim and G. ˙I¨oz, Gamma generalization operators involving analytic functions,
Mathematics, 9.13 (2021), 1547.
[2] A. Ciupa, A class of integral Favard-Szasz type operators, Studia Univ. Babes-Bolyai Math,
40 (1995), no.1, 3947.
[3] B. C¸ ekim, R. Akta¸s and F. Ta¸sdelen, A Dunkl-Gamma type operator in terms of generalization of two-variable Hermite polynomials Indian Journal of Pure and Applied Mathematics,
53 (2022), no.3, 727-735.
[4] N. Deo and S. Kumar, Durrmeyer variant of Apostol-Genocchi-Baskakov operators, Quaest.
Math. 44 (2020), no.4, 118.
[5] Neha and N. Deo, Integral modification of Apostol-Genocchi operators, Filomat, 35 (2021),
2533-2544.
[6] Neha and N. Deo, Integral modification of Beta-Apostol-Genocchi operators, Mathematical
Foundations of Computing, 6 (2023) no.3, 474-483.
[7] A.D. Gadjiev, The convergence problem for a sequence of positive linear operators on bounded
sets and theorems analogous to that of P.P. Korovkin, Doklady Akademii Nauk SSSR, 218
(1974) 1001-1004. (transl.in Sov. Math. Dokl. 15: 1433–1436.)
[8] I. Gavrea, I. Ra¸sa, Remarks on some quantitative Korovkin-type results, Rev. Anal. Numer.
Theor. Approx., 22 (1993) no.2, 173176 .
[9] S¸. G¨ung¨or, B. C¸ ekim, and M. Ozarslan, ¨ Approximation results for the operators involving
beta function and the Boas-Buck-Sheffer polynomials, Filomat, 38.1 (2024), 171187.
[10] A. Jakimovski, D. Leviatan, General Sz´asz operators for the approximation in the infinite
interval, Mathematica (Cluj) 34 (1969), 97-103.
[11] S. Karateke, C¸ . Atakut, ˙I. B¨uy¨ukyazıcı, Approximation by Generalized Integral Favard-Sz´asz
Type Operators Involving Sheffer Polynomials. Filomat 33 (2019), no.7, 19211935.
[12] P.P. Korovkin, On convergence of linear positive operators in the space of continuous functions, Dokl. Akad. Nauk SSSR. 90 953 (1953).
[13] Q. M. Luo and H. M. Srivastava, Some generalizations of the Apostol-Genocchi polynomials and the Stirling numbers of the second kind, Appl. Math. Comput. 217 (2011) no.12,
57025728.
[14] R. Malejki, and E. Wachnicki, On the Baskakov-Durrmeyer type operators, Commentationes
Mathematicae, 54 (2014) no.1, 39-49.
[15] S. M. Mazhar and V. Totik, Approximation by modified Sz´asz operators, Acta Scientiarum
Mathematicarum. 49 (1985), 257-269.
[16] N.S. Mishra and N. Deo, Approximation by a Composition of Apostol-Genocchi and PaltaneaDurrmeyer Operators. Kragujevac Journal of Mathematics 48 (2024), no.4, 629646.
[17] M.A. Ozarslan, O. Duman, ¨ Local approximation behavior of modified SMK operators, Miskolc
Math. Notes 11 (2010), no.1 8799.
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