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Approximation Properties of The Nonlinear Jain Operators

Year 2022, , 179 - 189, 22.12.2022
https://doi.org/10.36753/mathenot.983767

Abstract

We defined the nonlinear Jain operators of max-product type. We studied approximation properties of these operators.

References

  • [1] Bede, B., Coroianu, L., Gal, S. G.: Approximation and shape preserving properties of the Bernstein operator of max-product kind. Intern. J. Math. and Math. Sci. 26 pages (2009). doi:10.1155/2009/590589
  • [2] Bede, B., Gal, S. G.: Approximation by nonlinear Bernstein and Favard-Szasz- Mirakjan operators of max-product kind. Journal of Concrete and Applicable Mathematics. 8 (2), 193-207 (2010).
  • [3] Bede, B., Coroianu, L., Gal, S. G.: Approximation and shape preserving properties of the nonlinear Meyer-Konig and Zeller operator of max-product kind. Numerical Functional Analysis and Optimization. 31 (3), 232-253 (2010).
  • [4] Bede, B., Nobuhara, H., Fodor, J., Hirota, K.: Max-product Shepard approximation operators. Journal of Advanced Computational Intelligence and Intelligent Informatics. 10, 494-497 (2006).
  • [5] Bede, B., Nobuhara, H., Dankova, M., Di Nola, A.: Approximation by pseudo- linear operators. Fuzzy Sets and Systems. 159, 804-820 (2008).
  • [6] Bede, B., Coroianu, L., Gal, S. G.: Approximation by Max-Product Type Operators. Springer International Publishing. Switzerland (2016).
  • [7] Bede, B., Coroianu, L., Gal, S. G.: Approximation and shape preserving properties of the nonlinear Favard-Szasz- Mirakjan operator of max-product kind. Filomat. 24 (3), 55-72 (2010).
  • [8]Dog ̆ru,O.,Mohapatra,R.N.,Örkcü,M.:ApproximationpropertiesofgeneralizedJainoperators.Filomat.30(9), 2359-2366 (2016).
  • [9] Farcas A.: An Asymptotic Formula for Jain operators. Stud. Univ. Babes ̧-Bolyai Math. 57, 511-517 (2012).
  • [10] Gal,S.G.:Shape-PreservingApproximationbyRealandComplexPolynomials.Birkhauser.Boston-Basel-Berlin (2008).
  • [11] Jain, Gopi C.: Approximation of functions by a new class of linear operators. Journal of the Australian Mathematical Society. 13 (3) , 271-276 (1972).
  • [12] Özarslan, M.A.: Approximation properties of Jain-Stancu operators. Filomat. 30, 1081-1088 (2016).
  • [13] Olgun, A., Tas ̧delen, F., Erençin, A.: A generalization of Jain’s operators. Appl. Math. Comput. 266, 6-11 (2015).
  • [14] Mishra, V.N., Sharma, P., Kiliçman, A., Jain, D.: Statistical approximation properties of Stancu type q-Baskakov- Kantorovich operators. Filomat. 30 (7), 1853–1868 (2016).
  • [15] Mishra,V.N.,Patel,P.,Mishra,L.N.:TheIntegraltypeModificationofJainOperatorsanditsApproximationProperties. Numerical Functional Analysis and Optimization. 39 (12), 1265-1277 (2018).
  • [16] Mishra, V.N., Sharma, P., Birou, M.: Approximation by Modified Jain-Baskakov Operators. Georgian Mathematical Journal. 27 (3), 403-412 (2020).
  • [17] Mishra, V.N., Patel, P.: Some approximation properties of modified Jain-Beta operators. Journal of Calculus of Variations. Article ID 489249 (2013).
  • [18] Patel, P., Mishra, V.N.: Jain-Baskakov Operators and its different generalization. Acta Mathematica Vietnamica. 40 (4), 715–733, (2015).
  • [19] Patel, P., Mishra, V.N.: On Approximation properties of modified Sázas-Mirakyan operators via Jain Operators. Anal. Theory Appl. 32 (3), 232-241 (2016).
  • [20] Çiçek, H., Izgi, A., Ayhan, M. : GBS Operators of Bivariate Durrmeyer Operators on Simplex. Communications in Advanced Mathematical Sciences. Jan. 2021. https://dx.doi.org/10.33434/cams.932416 ̇
  • [21] Çiçek, H., Izgi, A.: The q-Chlodowsky and q-Szasz-Durrmeyer Hybrid Operators on Weighted Spaces. Journal of Mathematics. (2020). https://doi.org/10.1155/2020/8682598.
Year 2022, , 179 - 189, 22.12.2022
https://doi.org/10.36753/mathenot.983767

Abstract

References

  • [1] Bede, B., Coroianu, L., Gal, S. G.: Approximation and shape preserving properties of the Bernstein operator of max-product kind. Intern. J. Math. and Math. Sci. 26 pages (2009). doi:10.1155/2009/590589
  • [2] Bede, B., Gal, S. G.: Approximation by nonlinear Bernstein and Favard-Szasz- Mirakjan operators of max-product kind. Journal of Concrete and Applicable Mathematics. 8 (2), 193-207 (2010).
  • [3] Bede, B., Coroianu, L., Gal, S. G.: Approximation and shape preserving properties of the nonlinear Meyer-Konig and Zeller operator of max-product kind. Numerical Functional Analysis and Optimization. 31 (3), 232-253 (2010).
  • [4] Bede, B., Nobuhara, H., Fodor, J., Hirota, K.: Max-product Shepard approximation operators. Journal of Advanced Computational Intelligence and Intelligent Informatics. 10, 494-497 (2006).
  • [5] Bede, B., Nobuhara, H., Dankova, M., Di Nola, A.: Approximation by pseudo- linear operators. Fuzzy Sets and Systems. 159, 804-820 (2008).
  • [6] Bede, B., Coroianu, L., Gal, S. G.: Approximation by Max-Product Type Operators. Springer International Publishing. Switzerland (2016).
  • [7] Bede, B., Coroianu, L., Gal, S. G.: Approximation and shape preserving properties of the nonlinear Favard-Szasz- Mirakjan operator of max-product kind. Filomat. 24 (3), 55-72 (2010).
  • [8]Dog ̆ru,O.,Mohapatra,R.N.,Örkcü,M.:ApproximationpropertiesofgeneralizedJainoperators.Filomat.30(9), 2359-2366 (2016).
  • [9] Farcas A.: An Asymptotic Formula for Jain operators. Stud. Univ. Babes ̧-Bolyai Math. 57, 511-517 (2012).
  • [10] Gal,S.G.:Shape-PreservingApproximationbyRealandComplexPolynomials.Birkhauser.Boston-Basel-Berlin (2008).
  • [11] Jain, Gopi C.: Approximation of functions by a new class of linear operators. Journal of the Australian Mathematical Society. 13 (3) , 271-276 (1972).
  • [12] Özarslan, M.A.: Approximation properties of Jain-Stancu operators. Filomat. 30, 1081-1088 (2016).
  • [13] Olgun, A., Tas ̧delen, F., Erençin, A.: A generalization of Jain’s operators. Appl. Math. Comput. 266, 6-11 (2015).
  • [14] Mishra, V.N., Sharma, P., Kiliçman, A., Jain, D.: Statistical approximation properties of Stancu type q-Baskakov- Kantorovich operators. Filomat. 30 (7), 1853–1868 (2016).
  • [15] Mishra,V.N.,Patel,P.,Mishra,L.N.:TheIntegraltypeModificationofJainOperatorsanditsApproximationProperties. Numerical Functional Analysis and Optimization. 39 (12), 1265-1277 (2018).
  • [16] Mishra, V.N., Sharma, P., Birou, M.: Approximation by Modified Jain-Baskakov Operators. Georgian Mathematical Journal. 27 (3), 403-412 (2020).
  • [17] Mishra, V.N., Patel, P.: Some approximation properties of modified Jain-Beta operators. Journal of Calculus of Variations. Article ID 489249 (2013).
  • [18] Patel, P., Mishra, V.N.: Jain-Baskakov Operators and its different generalization. Acta Mathematica Vietnamica. 40 (4), 715–733, (2015).
  • [19] Patel, P., Mishra, V.N.: On Approximation properties of modified Sázas-Mirakyan operators via Jain Operators. Anal. Theory Appl. 32 (3), 232-241 (2016).
  • [20] Çiçek, H., Izgi, A., Ayhan, M. : GBS Operators of Bivariate Durrmeyer Operators on Simplex. Communications in Advanced Mathematical Sciences. Jan. 2021. https://dx.doi.org/10.33434/cams.932416 ̇
  • [21] Çiçek, H., Izgi, A.: The q-Chlodowsky and q-Szasz-Durrmeyer Hybrid Operators on Weighted Spaces. Journal of Mathematics. (2020). https://doi.org/10.1155/2020/8682598.
There are 21 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Articles
Authors

Sevilay Kırcı Serenbay 0000-0001-5819-9997

Özge Dalmanoğlu 0000-0002-0322-7265

Ecem Acar 0000-0002-2517-5849

Publication Date December 22, 2022
Submission Date August 17, 2021
Acceptance Date March 10, 2022
Published in Issue Year 2022

Cite

APA Kırcı Serenbay, S., Dalmanoğlu, Ö., & Acar, E. (2022). Approximation Properties of The Nonlinear Jain Operators. Mathematical Sciences and Applications E-Notes, 10(4), 179-189. https://doi.org/10.36753/mathenot.983767
AMA Kırcı Serenbay S, Dalmanoğlu Ö, Acar E. Approximation Properties of The Nonlinear Jain Operators. Math. Sci. Appl. E-Notes. December 2022;10(4):179-189. doi:10.36753/mathenot.983767
Chicago Kırcı Serenbay, Sevilay, Özge Dalmanoğlu, and Ecem Acar. “Approximation Properties of The Nonlinear Jain Operators”. Mathematical Sciences and Applications E-Notes 10, no. 4 (December 2022): 179-89. https://doi.org/10.36753/mathenot.983767.
EndNote Kırcı Serenbay S, Dalmanoğlu Ö, Acar E (December 1, 2022) Approximation Properties of The Nonlinear Jain Operators. Mathematical Sciences and Applications E-Notes 10 4 179–189.
IEEE S. Kırcı Serenbay, Ö. Dalmanoğlu, and E. Acar, “Approximation Properties of The Nonlinear Jain Operators”, Math. Sci. Appl. E-Notes, vol. 10, no. 4, pp. 179–189, 2022, doi: 10.36753/mathenot.983767.
ISNAD Kırcı Serenbay, Sevilay et al. “Approximation Properties of The Nonlinear Jain Operators”. Mathematical Sciences and Applications E-Notes 10/4 (December 2022), 179-189. https://doi.org/10.36753/mathenot.983767.
JAMA Kırcı Serenbay S, Dalmanoğlu Ö, Acar E. Approximation Properties of The Nonlinear Jain Operators. Math. Sci. Appl. E-Notes. 2022;10:179–189.
MLA Kırcı Serenbay, Sevilay et al. “Approximation Properties of The Nonlinear Jain Operators”. Mathematical Sciences and Applications E-Notes, vol. 10, no. 4, 2022, pp. 179-8, doi:10.36753/mathenot.983767.
Vancouver Kırcı Serenbay S, Dalmanoğlu Ö, Acar E. Approximation Properties of The Nonlinear Jain Operators. Math. Sci. Appl. E-Notes. 2022;10(4):179-8.

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