APPROXIMATION PROPERTIES OF MODIFIED SZASZ-SCHURER BASKAKOV TYPE OPERATORS

Year 2021, Volume: 2 Issue: 2, 83 - 96, 06.12.2021

Elif Şükrüoğlu , Ali Olgun

Abstract

In the present paper, we study some approximation properties of modified Szász-Schurer-Baskakov type operators. We estimate the moments for these operators using the Hypergeometric series, which are related to Laguerre polynomials. We give approximation properties of derivatives of these operators. Finally, we obtain the Voronovskaya type theorem for derivatives of these operators.

Keywords

Modified Szász-Schurer-Baskakov operator, Szász operator, point-wise convergence, approximation of derivatives, Modulus of continuity, Voronovskaya type theorem

References

• A. Aral, D. Inoan, I. Raşa, "On the Generalized Szász-Mirakjan Operators." Result Math. 65(3-4), 441-452 (2014).
• A. Erencin, G. Bascanbaz-Tunca, "Approximation Properties of a Class of Linear Positive Operators in Weighted Spaces" C. R. Acad. Bulg. Sci. 63(10) ,1397-1404,(2010)
• A. Erencin," DurrmeyerType Modification of Generalized Baskakov Operators." Appl. Math. comp. 218 (3), 4384-4390(2011)
• D.K. Verma, V. Gupta, P.N. Agrawal, "Some Approximation Properties of Baskakov-Durrmeyer-Stancu Operators" Appı. Math. and Comp. 218, 6549-6556, (2012)
• E. Pandey, R. K. Mishra, S.P. Pandey, "Approximation Properties of Some Modified Summation-İntegral Type Operator" Inter. Jour.of Soft Comp. and Eng.(IJSCE) ISSN:2231-2307, Volume-5, Issue-1, (2015)
• F. Altomare, M. Campiti, "Karovkin-type Approximation Theory and its Applications" Walter de Gruyter, Berlin. New York 1994
• F. Schurer, " Linear Positive Operators in Approximation Theory"Math. Inst. Techn. univ. Delfht. report.(1962)
• J.L. Durrmeyer, Une formule d'inversion de la transform~e de Laplace: Applications ~la th~orie des moments. Th~se de 3e cycle, Paris, (1967)
• Kumar, S., Acar, T." Approximation by generalized Baskakov-Durrmeyer-Stancu type operators", Rend.Circ.Mat. Palermo, 65(3), 2016.(E-SCI)
• N. Ispir, "Rate of Convergence of Generalized Rational Type Baskakov Operators"Math. Comp. Model 46, 625-631 (2007)
• O. Gürel Yılmaz, M. Bodur, A. Aral,"On Approximation Properties of Baskakov-Schurer-Szász Operators Preserving Exponantial Functions" Filomat, 32:15, 5433-5440(2018)
• P.N. Agrawal, V. Gupta, A.S. Kumar, "Generalized Baskakov-Durrmeyer Type Operators" Rend. Circ. Mat. Palermo, 63:193-209 (2014)
• R. Aktaş, B. Çekim, F. Taşdelen, "A Kantorovich-Stancu Type Generalization of Szasz operators Including Brenke-type Polynomials", Journal of Function Spaces and Applications, (2013), 9 pages
• R. Aktaş, D. Söylemez, F. Taşdelen, "Stancu type generalization of Szász-Durrmeyer operators involving Brenke-type polynomials",Filomat, 33 (3), 855-868 (2019).
• S. Arpaguş, A. Olgun " Approximation properties of Modified Baskakov Gamma Operators'' Facta Universitatis Mathematics and Informatics, (2020) (in press)
• S. Goldberg and V. Meir,"Mininmum Moduli of ordinary differential operators" Proc. London Math. Soc.,23, 1-15, (1971)
• T. Acar, V. Gupta, A. Aral,"Rate of Convergence for Generalized Szász Type Operators" Bull. Math. Sci.1(1), 99-113(2011)
• V. Gupta, M.A. Noor, M.S. Beniwal and M.K. Gupta "On Simultaneous Approximation for Certain Baskakov Durmeyer Type Operators" Jour. of İneq. in Pure and Appl. Math. Volum 7 Issue 4 Article 125 (2006)
• V. Gupta, D.K. Verma, P.N. Agrawal,"Simultaneous Approximation by Certain Baskako-Durrmeyer-Stancu Operators", Jour. of the Egyp. Math. Soc. 20-183-187(2012)
• V. N. Mishra, P. Sharma, "On Approximation Properties of Baskakov-Szász Operators", appl. Math. and. comp. v. 281, pp;381-393(2016)
• V. Gupta and G. S. Srivastava, "On the Convergence of Derivative by Szász-Mirakyan Baskakov Type Operators", The Math. Student64(1-49, 195-205(1995)
• V. Gupta and G. Tachev," Approximation by Szász-Mirakyan Baskakov Operators" J. Appl. Funct. Anal., 9(3-4) ,308-319(2014)