Research Article
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Year 2021, Volume: 70 Issue: 2, 924 - 939, 31.12.2021
https://doi.org/10.31801/cfsuasmas.898098

Abstract

References

  • Acar, E., Karahan, D., Kirci Serenbay, S., Approximation for the Bernstein operator of max-product kind in symmetric range, Khayyam J. Math., 6 (2) (2020), 257-273. DOI:10.22034/kjm.2020.109823
  • Agratini, O., On a sequence of linear and positive operators, Facta Univ. Ser. Math. Inform., 14 (1999), 41-48.
  • Bede, B., Nobuhara, H., Fodor, J., Hirota, K., Max-product Shepard approximation operators, Journal of Advanced Computational Intelligence and Intelligent Informatics, 10 (4) (2006), 494-497. DOI:10.20965/jaciii.2006.p0494
  • Bede, B., Nobuhara, H., Dankova , M., Di Nola, A., Approximation by pseudo- linear operators, Fuzzy Sets and Systems, 159 (2008), 804-820. DOI:10.1016/j.fss.2007.11.007
  • 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 (2010), 193-207.
  • Bede, B., Coroianu, L., Gal, S. G., Approximation by truncated Favard-Szasz-Mirakjan operator of max-product kind, Demonstratio Mathematica, 44 (1) (2011), 105-122. DOI:10.1515/dema-2013-0300
  • Bede, B., Coroianu, L., Gal, S. G., Approximation and shape preserving properties of the Bernstein operator of max-product kind, Int. J. Math. Math. Sci., 590589, (2009). DOI:10.1155/2009/590589
  • Coroianu, L.,Gal, S. G., Lp-approximation by truncated max-product sampling operators of Kantorovich-type based on Fejer kernel, Journal of Integral Equations and Applications, 29 (2) (2017), 349-364. DOI: 10.1216/JIE-2017-29-2-349
  • Coroianu, L., Gal, S. G., Approximation by truncated max-product operators of Kantorovich-type based on generalized $(\phi,\psi)$-kernels, Mathematical Methods in the Applied Sciences, DOI: 10.1002/mma.5262.
  • Coroianu, L., Gal, S. G., Approximation by max-product operators of Kantorovich type, Studia Universitatis Babes-Bolyai, Mathematica, 64 (2) (2019), 207-223. DOI:10.24193/subbmath.2019.2.07
  • Costarelli, D., Vinti, G., Convergence results for a family of Kantorovich max-product neural network operators in a multivariate setting, Math Slovaca, 67 (6) (2017), 1469-1480. DOI:10.1515/ms-2017-0063
  • Costarelli, D., Vinti, G., Estimates for the neural network operators of the max-product type with continuous and p-integrable functions, Results Math., 73 (12) (2018). DOI:10.1007/s00025-018-0790-0
  • Costarelli, D., Vinti, G., Approximation by max-product neural network operators of Kantorovich type, Results Math., 69 (1-2) (2016), 505-519. DOI: 10.1007/s00025-016-0546-7
  • Costarelli, D., Vinti, G., Saturation classes for max-product neural network operators activated by sigmoidal functions, Results Math, 72 (3), (2017), 1555-1569. DOI: 10.1007/s00025- 017-0692-6
  • Costarelli, D., Vinti, G., Max-product neural network and quasi interpolation operators activated by sigmoidal functions, J. Approx. Theory, 209 (2016), 1-22. DOI:10.1016/j.jat.2016.05.001
  • Duman, O., Statistical convergence of max-product approximating operators, Turkish Journal of Mathematics, 34 (4) (2010), 501-514. DOI:10.3906/mat-0807-32
  • Gal, S. G., Shape-Preserving Approximation by Real and Complex Polynomials, Birkhauser Publ. Co., Boston, Basel, Berlin, 2008. DOI: 10.1007/978-0-8176-4703-2
  • Güngör, Ş. Y., İspir N., Quantitative estimates for generalized Szasz operators of max product kind, Results in Mathematics, 70 (3) (2016), 447-456. DOI: 10.1007/s00025-016-0579-y
  • Güngör, Ş. Y., İspir N., Approximation by Bernstein-Chlodowsky operators of max-product kind, Mathematical Communications, 23 (2018), 205-225.
  • Holhoş, A., Weighted approximation of functions by Meyer-König and Zeller operators of max-product type, Numerical Functional Analysis and Optimization, 39 (6) (2018), 689-703. DOI: 10.1080/01630563.2017.1413386
  • Holhoş, A., Approximation of functions by Favard-Szasz-Mirakyan operators of max-product type in weighted spaces, Filomat, 32 (7) (2018), 2567-2576. DOI: 10.2298/FIL1807567H
  • Karakuş, S., Demirci, K., Statistical $\sigma$ approximation to max-product operators, Computers and Mathematics with Applications, 61 (4) (2011), 1024-1031. DOI:10.1016/j.camwa.2010.12.052
  • Lupaş, A., The approximation by some positive linear operators, In: Proceedings of the International Dortmund Meeting on Approximation Theory (M.W. Muller et al., eds.), Akademie Verlag, Berlin, (1995), 201-229.

Approximation by truncated Lupaş operators of max-product kind

Year 2021, Volume: 70 Issue: 2, 924 - 939, 31.12.2021
https://doi.org/10.31801/cfsuasmas.898098

Abstract

The goals of the present paper are to introduce truncated Lupaş type operators
of max-product kind and give an estimation for the degree of approximation with respect to
first modulus of continuity function. We prove that this estimate can not be
improved; on the other hand, for some subclasses of functions, better degree
of approximation is obtained. We also showed the piecewise convexity of the constructed operators on the interval [0,1].

References

  • Acar, E., Karahan, D., Kirci Serenbay, S., Approximation for the Bernstein operator of max-product kind in symmetric range, Khayyam J. Math., 6 (2) (2020), 257-273. DOI:10.22034/kjm.2020.109823
  • Agratini, O., On a sequence of linear and positive operators, Facta Univ. Ser. Math. Inform., 14 (1999), 41-48.
  • Bede, B., Nobuhara, H., Fodor, J., Hirota, K., Max-product Shepard approximation operators, Journal of Advanced Computational Intelligence and Intelligent Informatics, 10 (4) (2006), 494-497. DOI:10.20965/jaciii.2006.p0494
  • Bede, B., Nobuhara, H., Dankova , M., Di Nola, A., Approximation by pseudo- linear operators, Fuzzy Sets and Systems, 159 (2008), 804-820. DOI:10.1016/j.fss.2007.11.007
  • 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 (2010), 193-207.
  • Bede, B., Coroianu, L., Gal, S. G., Approximation by truncated Favard-Szasz-Mirakjan operator of max-product kind, Demonstratio Mathematica, 44 (1) (2011), 105-122. DOI:10.1515/dema-2013-0300
  • Bede, B., Coroianu, L., Gal, S. G., Approximation and shape preserving properties of the Bernstein operator of max-product kind, Int. J. Math. Math. Sci., 590589, (2009). DOI:10.1155/2009/590589
  • Coroianu, L.,Gal, S. G., Lp-approximation by truncated max-product sampling operators of Kantorovich-type based on Fejer kernel, Journal of Integral Equations and Applications, 29 (2) (2017), 349-364. DOI: 10.1216/JIE-2017-29-2-349
  • Coroianu, L., Gal, S. G., Approximation by truncated max-product operators of Kantorovich-type based on generalized $(\phi,\psi)$-kernels, Mathematical Methods in the Applied Sciences, DOI: 10.1002/mma.5262.
  • Coroianu, L., Gal, S. G., Approximation by max-product operators of Kantorovich type, Studia Universitatis Babes-Bolyai, Mathematica, 64 (2) (2019), 207-223. DOI:10.24193/subbmath.2019.2.07
  • Costarelli, D., Vinti, G., Convergence results for a family of Kantorovich max-product neural network operators in a multivariate setting, Math Slovaca, 67 (6) (2017), 1469-1480. DOI:10.1515/ms-2017-0063
  • Costarelli, D., Vinti, G., Estimates for the neural network operators of the max-product type with continuous and p-integrable functions, Results Math., 73 (12) (2018). DOI:10.1007/s00025-018-0790-0
  • Costarelli, D., Vinti, G., Approximation by max-product neural network operators of Kantorovich type, Results Math., 69 (1-2) (2016), 505-519. DOI: 10.1007/s00025-016-0546-7
  • Costarelli, D., Vinti, G., Saturation classes for max-product neural network operators activated by sigmoidal functions, Results Math, 72 (3), (2017), 1555-1569. DOI: 10.1007/s00025- 017-0692-6
  • Costarelli, D., Vinti, G., Max-product neural network and quasi interpolation operators activated by sigmoidal functions, J. Approx. Theory, 209 (2016), 1-22. DOI:10.1016/j.jat.2016.05.001
  • Duman, O., Statistical convergence of max-product approximating operators, Turkish Journal of Mathematics, 34 (4) (2010), 501-514. DOI:10.3906/mat-0807-32
  • Gal, S. G., Shape-Preserving Approximation by Real and Complex Polynomials, Birkhauser Publ. Co., Boston, Basel, Berlin, 2008. DOI: 10.1007/978-0-8176-4703-2
  • Güngör, Ş. Y., İspir N., Quantitative estimates for generalized Szasz operators of max product kind, Results in Mathematics, 70 (3) (2016), 447-456. DOI: 10.1007/s00025-016-0579-y
  • Güngör, Ş. Y., İspir N., Approximation by Bernstein-Chlodowsky operators of max-product kind, Mathematical Communications, 23 (2018), 205-225.
  • Holhoş, A., Weighted approximation of functions by Meyer-König and Zeller operators of max-product type, Numerical Functional Analysis and Optimization, 39 (6) (2018), 689-703. DOI: 10.1080/01630563.2017.1413386
  • Holhoş, A., Approximation of functions by Favard-Szasz-Mirakyan operators of max-product type in weighted spaces, Filomat, 32 (7) (2018), 2567-2576. DOI: 10.2298/FIL1807567H
  • Karakuş, S., Demirci, K., Statistical $\sigma$ approximation to max-product operators, Computers and Mathematics with Applications, 61 (4) (2011), 1024-1031. DOI:10.1016/j.camwa.2010.12.052
  • Lupaş, A., The approximation by some positive linear operators, In: Proceedings of the International Dortmund Meeting on Approximation Theory (M.W. Muller et al., eds.), Akademie Verlag, Berlin, (1995), 201-229.
There are 23 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Mediha Örkcü 0000-0002-0583-6005

Özge Dalmanoğlu 0000-0002-0322-7265

Fatma Büşra Hatipoğlu 0000-0003-0605-0466

Publication Date December 31, 2021
Submission Date March 17, 2021
Acceptance Date May 24, 2021
Published in Issue Year 2021 Volume: 70 Issue: 2

Cite

APA Örkcü, M., Dalmanoğlu, Ö., & Hatipoğlu, F. B. (2021). Approximation by truncated Lupaş operators of max-product kind. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 70(2), 924-939. https://doi.org/10.31801/cfsuasmas.898098
AMA Örkcü M, Dalmanoğlu Ö, Hatipoğlu FB. Approximation by truncated Lupaş operators of max-product kind. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. December 2021;70(2):924-939. doi:10.31801/cfsuasmas.898098
Chicago Örkcü, Mediha, Özge Dalmanoğlu, and Fatma Büşra Hatipoğlu. “Approximation by Truncated Lupaş Operators of Max-Product Kind”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70, no. 2 (December 2021): 924-39. https://doi.org/10.31801/cfsuasmas.898098.
EndNote Örkcü M, Dalmanoğlu Ö, Hatipoğlu FB (December 1, 2021) Approximation by truncated Lupaş operators of max-product kind. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70 2 924–939.
IEEE M. Örkcü, Ö. Dalmanoğlu, and F. B. Hatipoğlu, “Approximation by truncated Lupaş operators of max-product kind”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 70, no. 2, pp. 924–939, 2021, doi: 10.31801/cfsuasmas.898098.
ISNAD Örkcü, Mediha et al. “Approximation by Truncated Lupaş Operators of Max-Product Kind”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70/2 (December 2021), 924-939. https://doi.org/10.31801/cfsuasmas.898098.
JAMA Örkcü M, Dalmanoğlu Ö, Hatipoğlu FB. Approximation by truncated Lupaş operators of max-product kind. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70:924–939.
MLA Örkcü, Mediha et al. “Approximation by Truncated Lupaş Operators of Max-Product Kind”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 70, no. 2, 2021, pp. 924-39, doi:10.31801/cfsuasmas.898098.
Vancouver Örkcü M, Dalmanoğlu Ö, Hatipoğlu FB. Approximation by truncated Lupaş operators of max-product kind. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70(2):924-39.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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