The Pure and Applied Mathematics (한국수학교육학회지시리즈B:순수및응용수학)

Korean Society of Mathematical Education (한국수학교육학회)
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APPROXIMATION BY MODIFIED POST-WIDDER OPERATORS

  • Sheetal Deshwal (Department of Mathematics, Dr. Shivanand Nautiyal Goverment Post Graduate College) ;
  • Rupesh K. Srivastav (Department of Mathematics, Dr. Shivanand Nautiyal Goverment Post Graduate College) ;
  • Gopi Prasad (Department of Mathematics, Dr. Shivanand Nautiyal Goverment Post Graduate College)
  • Received : 2022.12.16
  • Accepted : 2023.01.25
  • Published : 2023.02.28
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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 modified operators as per classical Post-Widder operators is introduced in specific faculties also. Numerical examples are additionally introduced to verify our theortical results. In second last section we introduce Grüss-Voronovskaya results and in last section, we show the better approximation our new modified operators via graphical exmaples using Mathematica.

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References

  1. T. Acar: Quantitative q-Voronovskaya and q-Gruss-Voronovskaya-type results for q-Szasz operators. Georgian Math. J. 23 (2016), no. 4, 459-468. https://doi.org/10.1515/gmj-2016-0007
  2. T. Acar, A. Aral & I. Rasa: The new forms of Voronovskaja's theorem in weighted spaces. Positivity 20 (2016), 25-40. https://doi.org/10.1007/s11117-015-0338-4
  3. A.M. Acu, H. Gonska & I. Rasa: Gruss-type and Ostrowski-type inequalities in approximation theory. Ukrainian Math. J. 63 (2011), no. 6, 843-864. https://doi.org/10.1007/s11253-011-0548-2
  4. C. Atakut & N. Ispir: Approximation by modified Szasz-Mirakjan operators on weighted spaces. Proc. Indian Acad. Sci. Math. 112 (2002), 571-578. https://doi.org/10.1007/BF02829690
  5. E. Deniz: Quantitative estimates for Jain-Kantorovich operators. Commun. Fac. Sci. Univ. Ank. Sr. A1 Math. Stat. 65 (2016), 121-132. https://doi.org/10.1501/Commua1_0000000764
  6. S. Deshwal & P.N. Agrawal: Mihesan-Kantorovich operators of blending type. Gen. Math. 25 (2017), no.1-2, 11-27.
  7. Z. Ditzian & V. Totik: Moduli of smoothness. Springer-Verlag, New York, 1987.
  8. B.R. Draganov & K.G. Ivanov: A characterization of weighted approximations by the Post-Widder and the Gamma operators. J. Approx. Theory 146 (2007), 3-27. https://doi.org/10.1016/j.jat.2006.09.007
  9. 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./ Dokl. 15 (1974), no. 5, 1433-1436.
  10. S.G. Gal & H. Gonska: Gruss and Gruss-Voronovskaya-type esstimates for some Bernstein-type polynomials of real and complex variables. Jaen J. Approx. 7 (2015), 97-122.
  11. H. Gonska & G. Tachev: Gruss type inequality for positive linear operators with second order moduli. Mat. Vesnik 63 (2011), no. 4, 247-252.
  12. G. Gruss: Uber das Maximum des absoluten Betrages von $\frac{1}{b-a}\int_{a}^{b}f(x)g(x)dx$-$\frac{1}{(b-a)^2}\int_{a}^{b}f(x)dx$. $\int_{a}^{b}g(x)dx$. Math. Z. 39 (1935), 215-226. https://doi.org/10.1007/BF01201355
  13. V. Gupta & D. Agrawal: Convergence by modified Post-Widder operators. RACSAM. 113 (2019), no. 2, 1475-1486. https://doi.org/10.1007/s13398-018-0562-4.
  14. V. Gupta & G. Tachev: Some results on Post-Widder operators preserving test function xr. Kragujevac J. Math. 46 (2022), no. 1, 149-165. https://doi.org/10.46793/KgJMat2201.149G
  15. A. Kajla, S. Deshwal & P.N. Agrawal: Quantitative Voronovskaya and GrssVoronovskaya type theorems for JainDurrmeyer operators of blending type. Anal. Math. Phys. 9 (2019), 12411263. https://doi.org/10.1007/s13324-018-0229-5.
  16. C.P. May: Saturation and inverse theorems for combinations of a class of exponential type operators. Canad. J. Math. 28 (1976), 1224-1250. https://doi.org/10.4153/CJM-1976-123-8
  17. R.K.S. Rathore & O.P. Singh: On convergence of derivatives of Post-Widderoperators. Indian J. Pure Appl. Math. 11 (1980), 547-561.
  18. R.K. Srivastav & S. Deshwal: Convergence : new Post-Widder operators. Int. J. Math. Trends Tech. 67 (2021), no. 2, 43-52. https://doi.org/10.14445/22315373/IJMTT-V67I2P507
  19. G. Prasad: Coincidence points of relational Ψ-contractions and an application. Afr. Math. 32 (2021), no. 6-7, 1475-1490. https://doi.org/10.1007/s13370-021-00913-6
  20. L. Rempulska & M. Skorupka: On strong approximation applied to Post-Widder operators. Anal. Theory Appl. 22 (2006), 172-182. https://doi.org/10.1007/BF03218710
  21. M. Sofyalioglu & K. Kanat: Approximation properties of the Post-Widder operators preserving e2ax, a > 0. Math. Mathods Appl. Sci. 43 (2020), no. 7, 4272-4285. DOI:10.1002/mma.6192.
  22. J. Taiboon & K.N. Ntouyas: Quantum integral inequalities on finite intervals. J. Inequal. Appl. 2014 (2014), Article ID 121.
  23. G. Ulusoy & T. Acar: q-Voronovskaya type theorems for q-Baskakov operators, Math. Methods Appl. Sci. 39 (2015), no. 12 3391-3401. DOI 10.1002/mma.3785.