Abstract
In the present paper, we discuss the approximation properties of certain link integral modification of Ismail–May operators. We point out here that the operators of Ismail–May can also be derived from the Jain operators. We also establish some direct convergence estimates including error, difference estimates and an asymptotic formula in simultaneous approximation. In the end, we indicate through graphical representation the convergence of polynomial function with the link operators.
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Acu, A.M., Gupta, V., Tachev, G.: Better numerical approximation by Durrmeyer type operators. Results Math. 74(3), 90 (2019)
Altomare, F., Rasa, I.: On a class of exponential-type operators and their limit semigroups. J. Approx. Theory 135, 258–275 (2005)
DeVore, R.A., Lorentz, G.G.: Constructive Approximation. Springer, Berlin (1993)
Garg, T., Acu, A.M., Agrawal, P.N.: Further results concerning some general Durrmeyer type operators. Rev. Real Acad. Cie. Exactas Fís. Nat. Ser. A. Mat. 113(3), 2373–2390 (2019)
Gupta, V.: On difference of operators with applications to Szász type operators. Rev. Real Acad. Cie. Exactas Fís. Nat. Ser. A. Mat. 113(3), 2059–2071 (2019)
Gupta, V., Acu, A.M.: On difference of operators with different basis functions. Filomat 33, 10 (2019)
Gupta, V., Greubel, G.C.: Moment estimations of a new Szasz–Mirakyan–Durrmeyer operators. Appl. Math Comput. 271, 540–547 (2015)
Gupta, V., Rassias, M.T.: Moments of Linear Positive Operators and Approximation. Springer Briefs in Mathematics. Springer, Geneva (2019)
Gupta, V., Rassias, T.M., Agrawal, P.N., Acu, A.M.: Estimates for the differences of positive linear operators. Recent Advances in Constructive Approximation Theory. Springer Optimization and Its Applications, vol. 138. Springer, Cham (2018)
Ismail, M.: Polynomials of binomial type and approximation theory. J. Approx. Theory 23, 177–186 (1978)
Ismail, M., May, C.P.: On a family of approximation operators. J. Math. Anal. Appl. 63, 446–462 (1978)
Jain, G.C.: Approximation of functions by a new class of linear operators. J. Austral. Math. Soc. 13, 271–276 (1972)
Pǎltǎnea, R.: Modified Sz\(\acute{a}\)sz–Mirakjan operators of integral form. Carpathian J. Math. 24(3), 378–385 (2008)
Pǎltǎnea, R.: Simultaneous approximation by a class of Szász Mirakjan operators. J. Appl. Funct. Anal. 9(3–4), 356–368 (2014)
Polya, G., Szagö, G.: Problems and Theorems in Analysis, XIX, vol. 392. Springer, New York (1972)
Pop, O.T., Fǎrcaş, M.D.: About a class of linear positive operators. Gener. Math. 16(1), 59–72 (2008)
Sato, K.: Global approximation theorems for some exponential-type operators. J. Approx. Theory 32, 32–46 (1981)
Totik, V.: Uniform approximation by exponential-type operators. J. Math. Anal. Appl. 132, 238–246 (1988)
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The authors are extremely thankful to the reviewers for their valuable suggestions, leading to overall improvements in the manuscript.
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Communicated by Gradimir Milovanovic.
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Gupta, V., Agrawal, G. Approximation for link Ismail–May operators. Ann. Funct. Anal. 11, 728–747 (2020). https://doi.org/10.1007/s43034-019-00051-y
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DOI: https://doi.org/10.1007/s43034-019-00051-y
Keywords
- Ismail–May operators
- Jain operators
- Convergence estimates
- Difference estimates
- Simultaneous approximation