Approximation by an Exponential-Type Complex Operators
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Authors: S. G. GAL AND V. GUPTA
DOI: 10.46793/KgJMat2305.691G
Abstract:
In the present paper, we discuss the approximation properties of a complex exponential kind operator. Upper estimate, Voronovskaya-type formula and exact estimate are obtained.
Keywords:
Complex exponential kind operator, approximation properties, upper estimate, Voronovskaya-type formula, exact estimate.
References:
[1] T. Acar, Asymptotic formulas for generalized Szász-Mirakyan operators, Appl. Math. Comput. 263 (2015), 233–239. https://doi.org/10.1016/j.amc.2015.04.060
[2] R. P. Agarwal and V. Gupta, On q-analogue of a complex summation-integral type operators in compact disks, J. Inequal. Appl. 2012(1) (2012), Article ID 111. https://doi.org/10.1186/1029-242X-2012-111
[3] S. G. Gal and V. Gupta, Quantitative estimates for a new complex Durrmeyer operator in compact disks, Appl. Math. Comput. 218(6) (2011), 2944–2951. https://doi.org/10.1016/j.amc.2011.08.044
[4] S. G. Gal, V. Gupta and N. I. Mahmudov, Approximation by a Durrmeyer-type operator in compact disks, Ann. Univ. Ferrara Sez. VII Sci. Mat. 58(2) (2012), 65–87. https://doi.org/10.1007/s11565-011-0124-6
[5] S. G. Gal and V. Gupta, Approximation by a complex Post-Widder type operator, Anal. Theory Appl. 34(4) (2018), 297–305. https://doi.org/10.4208/ata.OA-2018-0003
[6] S. G. Gal, Approximation by Complex Bernstein and Convolution Type Operators, World Scientific, 2009. https://doi.org/10.1142/7426
[7] S. G. Gal, Overconvergence in Complex Approximation, Springer, New York, 2013. https://doi.org/10.1007/978-1-4614-7098-4
[8] V. Gupta, Approximation with certain exponential operators, Rev. R. Acad. Cienc. Exactas Fis. Nat. Ser. A Mat. RACSAM 114(2) (2020). https://doi.org/10.1007/s13398-020-00792-9
[9] V. Gupta and R. P. Agarwal, Convergence Estimates in Approximation Theory, Springer, Cham, 2014. https://doi.org/10.1007/978-3-319-02765-4
[10] M. Ismail, Polynomials of binomial type and approximation theory, J. Approx. Theory 23(1978), 177–186. https://doi.org/10.1016/0021-9045(78)90105-3
[11] M. Ismail and C. P. May, On a family of approximation operators, J. Math. Anal. Appl. 63 (1978), 446–462. https://doi.org/10.1016/0022-247X(78)90090-2
[12] A. S. Kumar, P. N. Agrawal and T. Acar, Quantitative estimates for a new complex q-Durrmeyer type operators on compact disks, UPB Scientific Bulletin, Series A 80(1) (2018), 191–210.
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