Approximation by Modified Post-Widder Operators
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초록
The current article manages with new generalization of Post-Widder operators preserving constant function and other test functions in Bohmann-Korovkin sense and studies the approximation properties via different estimation tools like modulus of continuity and approximation in weighted spaces. The viability of the recently modi fied operators as per classical Post-Widder operators is introduced in specifi c faculties also. Numerical examples are additionally introduced to verify our theoretical results. In second last section we introduce Gruss-Voronovskaya results and in last section, we show the better approximation our new modi fied operators via graphical examples using Mathematica.
Abstract
The current article manages with new generalization of Post-Widder operators preserving constant function and other test functions in Bohmann-Korovkin sense and studies the approximation properties via different estimation tools like modulus of continuity and approximation in weighted spaces. The viability of the recently modi fied operators as per classical Post-Widder operators is introduced in specifi c faculties also. Numerical examples are additionally introduced to verify our theoretical results. In second last section we introduce Gruss-Voronovskaya results and in last section, we show the better approximation our new modi fied operators via graphical examples using Mathematica.
참고문헌 (23)
- T. Acar, "Quantitative q-Voronovskaya and q-Gruss-Voronovskaya-type results for q-Szasz operators", Georgian Math. J, 23(4), pp.459~468 (2016)
- T. Acar, "The new forms of Voronovskaja's theorem in weighted spaces", Positivity, 20, pp.25~40 (2016)
- A.M. Acu, "Gruss-type and Ostrowski-type inequalities in ap-proximation theory", Ukrainian Math. J, 63(6), pp.843~864 (2011)
- C. Atakut, "Approximation by modified Szasz-Mirakjan operators on weighted spaces", Proc. Indian Acad. Sci. Math, 112, pp.571~578 (2002)
- E. Deniz, "Quantitative estimates for Jain-Kantorovich operators", Commun. Fac. Sci. Univ. Ank. Sr. A1 Math. Stat, 65, pp.121~132 (2016)
- S. Deshwal, "Mihesan-Kantorovich operators of blending type", Gen. Math, 25(1-2), pp.11~27 (2017)
- Z. Ditzian, "Moduli of smoothness" (1987), Springer-Verlag
- B.R. Draganov, "A characterization of weighted approximations by the Post-Widder and the Gamma operators", J. Approx. Theory, 146, pp.3~27 (2007)
- A.D. Gadzhiev, "The convergence problem for a sequence of positive linear operators on unbounded sets and theorem analogue to that of P.P. Korovkin", Soviet Math., 1974, pp.15(5), 1433~1436
- S.G. Gal, "Gruss and Gruss-Voronovskaya-type esstimates for some Bernstein-type polynomials of real and complex variables", Jaen J. Approx, 7, pp.97~122 (2015)
- H. Gonska, "Gruss type inequality for positive linear operators with second order moduli", Mat. Vesnik, 63(4), pp.247~252 (2011)
- G. Gruss, "Über das Maximum des absoluten Betrages von 1b−a ∫ b a f (x)g(x)dx − 1(b−a)2 ∫ ba f(x)dx ∫ b a g(x)dx", Math. Z, 39, pp.215~226 (1935)
- Vijay Gupta, "Convergence by modified Post-Widder operators", Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas, 113(2), pp.1475~1486 (2018), Springer Science and Business Media LLC[DOI]
- V. Gupta, "Some results on Post-Widder operators preserving test function xr", Kragujevac J. Math, 46(1), pp.149~165 (2022)
- Arun Kajla, "Quantitative Voronovskaya and Grüss-Voronovskaya type theorems for Jain–Durrmeyer operators of blending type", Analysis and Mathematical Physics, 9(3), pp.1241~1263 (2018), Springer Science and Business Media LLC[DOI]
- C. P. May, "Saturation and inverse theorems for combinations of a class of exponential type operators", Canad. J. Math, 28, pp.1224~1250 (1976)
- R.K.S. Rathore, "On convergence of derivatives of Post-Widderoperators", Indian J. Pure Appl. Math, 11, pp.547~561 (1980)
- R.K. Srivastav, "Convergence : new Post-Widder operators", Int. J. Math. Trends Tech, 67(2), pp.43~52 (2021)
- G. Prasad, "Coincidence points of relational ψ-contractions and an application", Afr. Math, 32(6-7), pp.1475~1490 (2021)
- L. Rempulska, "On strong approximation applied to Post-Widder op-erators", Anal. Theory Appl, 22, pp.172~182 (2006)
- Melek Sofyalıoğlu, "Approximation properties of the Post‐Widder operators preserving e2ax,a>0", Mathematical Methods in the Applied Sciences, 43(7), pp.4272~4285 (2020), Wiley[DOI]
- J. Taiboon, "Quantum integral inequalities on finite intervals", J. In-equal. Appl, 2014 (2014)
- G. Ulusoy, "q-Voronovskaya type theorems for q-Baskakov operators", Math. Methods Appl. Sci, 39(12), pp.3391~3401 (2015)[DOI]