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Kantorovich Stancu Type Operator Including Generalized Brenke Polynomials

Year 2023, Volume: 10 Issue: 4, 555 - 570, 31.12.2023

Gurhan İçöz Shamsullah Zaland

https://doi.org/10.54287/gujsa.1386488

Abstract

This article is concerned with the sequence of operators of Stancu’s-type, involving extended Brenke polynomials. We apply Korovkin’s theorem to the sequence of positive linear operators, discuss the uniform approximation of continuous functions on closed bounded intervals by known tools theory, and also consider the second modulus of continuity, Peetre’s K-functional and Lipschitz class, which are essential concepts in approximation theory.

Keywords

Stancu-Type Operators Sucu Operators Kantorovich Type of the Operators Kantorovich Stancu Type Linear Positive Operators

References

  • Agrawal, P. N., Baxhaku, B., & Chauhan, R. (2018). Quantitative Voronovskaya-and Grüss-Voronovskaya-type theorems by the blending variant of Szász operators including Brenke-type polynomials. Turkish Journal of Mathematics, 42(4), 1610-1629. https://doi.org/10.3906/mat-1708-1
  • Aktaş¸ R., Çekim, B., & Taşdelen, F. (2013). A Kantorovich-Stancu Type Generalization of Szász Operators including Brenke Type Polynomials. Journal of Function Spaces and Applications, 935430. https://doi.org/10.1155/2013/935430
  • Atakut, Ç., & Büyükyazcı, İ. (2016). Approximation by Kantorovich-Szász type operators based on Brenke type polynomials. Numerical Functional Analysis and Optimization, 37(12), 1488-1502. https://doi.org/10.1080/01630563.2016.1216447
  • Chaggaraa, H., & Gahami, A. (2023). Classification of 2-Orthogonal Polynomials with Brenke Type Generating Functions. Mathematical Physics. https://doi.org/10.48550/arXiv.2310.11734
  • Cheney, E. W., & Sharma, A. (1964). Bernstein power series. Canadian Journal of Mathematics, 16, 241-252. https://doi.org/10.4153/CJM-1964-023-1
  • Çekim, B., Aktaş, R., & İçöz, G. (2019). Kantrovich-Stancu type operators including Boas-Buck type polynomials. Hacettepe Journal of Mathematics and Statistics, 48(2), 460-471. https://doi.org/10.15672/HJMS.2017.528
  • İçöz, G., & Çekim, B. (2015). Dunkl generalization of Szász operators via q-calculus. Journal of Inequalities and Applications, 284. https://doi.org/10.1186/s13660-015-0809-y
  • İçöz, G., & Çekim, B. (2016a). Stancu type generalization of Dunkl analogue of Szász Kantorovich operators. Mathematical Methods in the Applied Sciences, 39(7), 1803-1810. https://doi.org/10.1002/mma.3602
  • İçöz, G., & Çekim, B. (2016b). Stancu-type generalization of the Chan-Chyan-Srivastava operators. Filomat, 30(14), 3733-3742. https://doi.org/10.2298/FIL1614733I
  • İçöz, G., & Eryigit, H. (2020). Beta generalization of Stancu-Durrmeyer operators involving a generalization of Boas-Buck type polynomials. Gazi University Journal of Science, 33(3), 715-724. https://doi.org/10.35378/gujs.597272
  • İçöz, G., Varma, S., & Sucu, S. (2016). Approximation by operators including Generalized Appell polynomials. Filomat, 30(2), 429-440. https://doi.org/10.2298/FIL1602429I
  • Jakimovski, A., & Leviatan, D. (1969). Generalized Szász operators for the approximation in the infinite interval. Mathematica (Cluj), 11(34), 97-103.
  • Rao, N., Heshamuddin, Md., Shadab, M., & Srivastava A. (2021). Approximation Properties of Bivariate Szász Durrmeyer Operators via Dunkl Analogue. Filomat, 35(13), 4515-4532. https://doi.org/10.2298/FIL2113515R
  • Srivasta, N., İçöz, G., & Çekim, B. (2019). Approximation properties of on extended family of the Szász Mirakjan Beta type operators. Axioms, 8(4), 111. https://doi.org/10.3390/axioms8040111
  • Sucu, S. (2022). Stancu type operators including generalized Brenke polynomials. Filomat, 36(07), 2381-2389. https://doi.org/10.2298/FIL2207381S
  • Sucu, S., & Varma, S. (2019). Approximation by sequence of operators involving analytic functions. Mathematics, 7(2), 188. https://doi.org/10.3390/math7020188
  • Sucu, S., İçöz, G., & Varma, S. (2012). On some extensions of Szász operators including Boas-Buck-type polynomials. Abstract and Applied Analysis, 680340. https://doi.org/10.1155/2012/680340
  • Varma, S. (2013). On a generalization of Szász operators by multiple Appell polynomials. Stud. Univ. Babeş-Bolyai Math, 58(3), 361-369
  • Varma, S., & Sucu, S. (2022). Operators obtained by using certain generating function for approximation. Mathematics, 10(13), 2239. https://doi.org/10.3390/math10132239
  • Varma, S., Sucu, S., & İçöz, G. (2012). Generalization of Szász operators involving Brenke type polynomials. Computers and Mathematics with Applications, 64(2), 121-127. https://doi.org/10.1016/j.camwa.2012.01.025

Year 2023, Volume: 10 Issue: 4, 555 - 570, 31.12.2023

Gurhan İçöz Shamsullah Zaland

https://doi.org/10.54287/gujsa.1386488

Abstract

References

  • Agrawal, P. N., Baxhaku, B., & Chauhan, R. (2018). Quantitative Voronovskaya-and Grüss-Voronovskaya-type theorems by the blending variant of Szász operators including Brenke-type polynomials. Turkish Journal of Mathematics, 42(4), 1610-1629. https://doi.org/10.3906/mat-1708-1
  • Aktaş¸ R., Çekim, B., & Taşdelen, F. (2013). A Kantorovich-Stancu Type Generalization of Szász Operators including Brenke Type Polynomials. Journal of Function Spaces and Applications, 935430. https://doi.org/10.1155/2013/935430
  • Atakut, Ç., & Büyükyazcı, İ. (2016). Approximation by Kantorovich-Szász type operators based on Brenke type polynomials. Numerical Functional Analysis and Optimization, 37(12), 1488-1502. https://doi.org/10.1080/01630563.2016.1216447
  • Chaggaraa, H., & Gahami, A. (2023). Classification of 2-Orthogonal Polynomials with Brenke Type Generating Functions. Mathematical Physics. https://doi.org/10.48550/arXiv.2310.11734
  • Cheney, E. W., & Sharma, A. (1964). Bernstein power series. Canadian Journal of Mathematics, 16, 241-252. https://doi.org/10.4153/CJM-1964-023-1
  • Çekim, B., Aktaş, R., & İçöz, G. (2019). Kantrovich-Stancu type operators including Boas-Buck type polynomials. Hacettepe Journal of Mathematics and Statistics, 48(2), 460-471. https://doi.org/10.15672/HJMS.2017.528
  • İçöz, G., & Çekim, B. (2015). Dunkl generalization of Szász operators via q-calculus. Journal of Inequalities and Applications, 284. https://doi.org/10.1186/s13660-015-0809-y
  • İçöz, G., & Çekim, B. (2016a). Stancu type generalization of Dunkl analogue of Szász Kantorovich operators. Mathematical Methods in the Applied Sciences, 39(7), 1803-1810. https://doi.org/10.1002/mma.3602
  • İçöz, G., & Çekim, B. (2016b). Stancu-type generalization of the Chan-Chyan-Srivastava operators. Filomat, 30(14), 3733-3742. https://doi.org/10.2298/FIL1614733I
  • İçöz, G., & Eryigit, H. (2020). Beta generalization of Stancu-Durrmeyer operators involving a generalization of Boas-Buck type polynomials. Gazi University Journal of Science, 33(3), 715-724. https://doi.org/10.35378/gujs.597272
  • İçöz, G., Varma, S., & Sucu, S. (2016). Approximation by operators including Generalized Appell polynomials. Filomat, 30(2), 429-440. https://doi.org/10.2298/FIL1602429I
  • Jakimovski, A., & Leviatan, D. (1969). Generalized Szász operators for the approximation in the infinite interval. Mathematica (Cluj), 11(34), 97-103.
  • Rao, N., Heshamuddin, Md., Shadab, M., & Srivastava A. (2021). Approximation Properties of Bivariate Szász Durrmeyer Operators via Dunkl Analogue. Filomat, 35(13), 4515-4532. https://doi.org/10.2298/FIL2113515R
  • Srivasta, N., İçöz, G., & Çekim, B. (2019). Approximation properties of on extended family of the Szász Mirakjan Beta type operators. Axioms, 8(4), 111. https://doi.org/10.3390/axioms8040111
  • Sucu, S. (2022). Stancu type operators including generalized Brenke polynomials. Filomat, 36(07), 2381-2389. https://doi.org/10.2298/FIL2207381S
  • Sucu, S., & Varma, S. (2019). Approximation by sequence of operators involving analytic functions. Mathematics, 7(2), 188. https://doi.org/10.3390/math7020188
  • Sucu, S., İçöz, G., & Varma, S. (2012). On some extensions of Szász operators including Boas-Buck-type polynomials. Abstract and Applied Analysis, 680340. https://doi.org/10.1155/2012/680340
  • Varma, S. (2013). On a generalization of Szász operators by multiple Appell polynomials. Stud. Univ. Babeş-Bolyai Math, 58(3), 361-369
  • Varma, S., & Sucu, S. (2022). Operators obtained by using certain generating function for approximation. Mathematics, 10(13), 2239. https://doi.org/10.3390/math10132239
  • Varma, S., Sucu, S., & İçöz, G. (2012). Generalization of Szász operators involving Brenke type polynomials. Computers and Mathematics with Applications, 64(2), 121-127. https://doi.org/10.1016/j.camwa.2012.01.025
There are 20 citations in total.

Details

Primary Language English
Subjects Applied Mathematics (Other)
Journal Section Mathematics
Authors

Gurhan İçöz 0000-0003-1204-9517

Shamsullah Zaland 0000-0002-7548-9483

Publication Date December 31, 2023
Submission Date November 5, 2023
Acceptance Date December 27, 2023
Published in Issue Year 2023 Volume: 10 Issue: 4

Cite

APA İçöz, G., & Zaland, S. (2023). Kantorovich Stancu Type Operator Including Generalized Brenke Polynomials. Gazi University Journal of Science Part A: Engineering and Innovation, 10(4), 555-570. https://doi.org/10.54287/gujsa.1386488
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