Approximation Results of Nonlinear Operators via Power Series Statistical Convergence in Modular Space

Emre Taş; Sevil Aykanat

doi:10.47000/tjmcs.1794000

Approximation Results of Nonlinear Operators via Power Series Statistical Convergence in Modular Space

Abstract

In the setting of modular spaces, we present a Korovkin-type approximation theorem for a class of nonlinear operators by employing power series statistical convergence. An illustrative example is also provided to demonstrate the applicability of the main result.

Keywords

References

Arif, A., Yurdakadim, T. Approximation results on nonlinear operators by Pp-statistical convergence, Adv. Stud. Euro-Tbil. Math. J., 15(2022), 1–10.
Aslan, I. Convergence in phi-variation and rate of approximation for nonlinear integral operators using summability process, Mediterr. J. Math., 18(2021), Paper No. 5.
Aslan, I., Duman, O. Nonlinear approximation in N-dimension with the help of summability methods, RACSAM, 115(2021), Paper No. 105.
Bardaro, C., Mantellini, I. Korovkin theorem in modular spaces, Comment. Math., 47(2007), 239–253.
Bardaro, C., Mantellini, I. Multivariate moment type operators: approximation properties in Orlicz spaces, J. Math. Inequal., 2(2008), 247–259.
Bardaro, C., Mantellini, I. A Korovkin theorem in multivariate modular function spaces, J. Funct. Spaces Appl., 2(2009), 105–120.
Bardaro, C., Boccuto, A., Dimitriou, X., Mantellini, I. Abstract Korovkin-type theorems in modular spaces and applications, Cent. Eur. J. Math., 11(2013), 1774–1784.
Boos, J. Classical and Modern Methods in Summability, Oxford Univ. Press, 2000.

Fridy, J.A., Orhan, C. Statistical limit superior and limit inferior, Proc. Amer. Math. Soc., 125(1997), 3625–3631.
Gal, S.G. Uniform and pointwise quantitative approximation by Kantorovich-Choquet type integral operators with respect to monotone and submodular set functions, Mediterr. J. Math., 14(2017), 205–216.
Gal, S.G., Niculescu, C.P. A nonlinear extension of Korovkin’s theorem, Mediterr. J. Math., 17(2020), Paper No. 145.
Gal, S.G., Niculescu, C.P. Korovkin-type theorems for weakly nonlinear and monotone operators, Mediterr. J. Math., 20(2023), 56.
Gökçer, T.Y., Duman, O. Approximation by max-min operators: A general theory and its applications, Fuzzy Sets Syst., 394(2020), 146–161.
Karakus, S., Demirci, K., Duman, O. Statistical approximation by positive linear operators on modular spaces, Positivity, 14(2010), 321–334.
Korovkin, P.P., Linear Operators and Approximation Theory, Hindustan Publ. Corp., Delhi, 1960.
Kratz, W., Stadtm¨uller, U. Tauberian theorems for Jp-summability, J. Math. Anal. Appl., 139(1989), 362–371.
Musielak, J., Orlicz Spaces and Modular Spaces, Springer-Verlag, Berlin, 1983.
Stadtmüller, U., Tali, A. On certain families of generalized N¨orlund methods and power series methods, J. Math. Anal. Appl., 238(1999), 44–66.
Unver, M., Orhan, C. Statistical convergence with respect to power series methods and applications to approximation theory, Numer. Funct. Anal. Optim., 40(2019), 535–547.
Taş, E., Aykanat, S. Some approximation results for nonlinear operators in modular space, Adv. Stud. Euro-Tbil. Math. J., Accepted.
Taş, E., Yurdakadim, T. Approximation results by statistical convergence based on a power series in modular spaces, Lobachevskii J. Math., 44(2023), 4913–4919.
Taş, E., Yurdakadim, T. Approximation by positive linear operators in modular spaces by power series method, Positivity, 21(2017), 1293–1306.
Yıldız, S., Demirci, K., Dirik, F. Approximation theorems via power series statistical convergence and applications for sequences of monotone and sublinear operators, Rev. R. Acad. Cienc. Exactas F´ıs. Nat. Ser. A-Mat., (2025) 119(100).
Yurdakadim, T. Abstract Korovkin theory in modular spaces in the sense of power series method, Hacet. J. Math. Stat., 47(2018), 1467–1477.

Details

Primary Language

English

Subjects

Approximation Theory and Asymptotic Methods

Journal Section

Research Article

Authors

Emre Taş ^*
0000-0002-6569-626X
Türkiye

Sevil Aykanat
0000-0002-5999-2281
Türkiye

Publication Date

February 23, 2026

Submission Date

September 30, 2025

Acceptance Date

November 17, 2025

Published in Issue

Year 2026 Volume: 18 Number: 1

DOI

https://doi.org/10.47000/tjmcs.1794000

IZ

https://izlik.org/JA97BN73CM

Cite

RIS / Bibtex

APA

Taş, E., & Aykanat, S. (2026). Approximation Results of Nonlinear Operators via Power Series Statistical Convergence in Modular Space. Turkish Journal of Mathematics and Computer Science, 18(1), 111-119. https://doi.org/10.47000/tjmcs.1794000

AMA

1.Taş E, Aykanat S. Approximation Results of Nonlinear Operators via Power Series Statistical Convergence in Modular Space. TJMCS. 2026;18(1):111-119. doi:10.47000/tjmcs.1794000

Chicago

Taş, Emre, and Sevil Aykanat. 2026. “Approximation Results of Nonlinear Operators via Power Series Statistical Convergence in Modular Space”. Turkish Journal of Mathematics and Computer Science 18 (1): 111-19. https://doi.org/10.47000/tjmcs.1794000.

EndNote

Taş E, Aykanat S (February 1, 2026) Approximation Results of Nonlinear Operators via Power Series Statistical Convergence in Modular Space. Turkish Journal of Mathematics and Computer Science 18 1 111–119.

IEEE

[1]E. Taş and S. Aykanat, “Approximation Results of Nonlinear Operators via Power Series Statistical Convergence in Modular Space”, TJMCS, vol. 18, no. 1, pp. 111–119, Feb. 2026, doi: 10.47000/tjmcs.1794000.

ISNAD

Taş, Emre - Aykanat, Sevil. “Approximation Results of Nonlinear Operators via Power Series Statistical Convergence in Modular Space”. Turkish Journal of Mathematics and Computer Science 18/1 (February 1, 2026): 111-119. https://doi.org/10.47000/tjmcs.1794000.

JAMA

1.Taş E, Aykanat S. Approximation Results of Nonlinear Operators via Power Series Statistical Convergence in Modular Space. TJMCS. 2026;18:111–119.

MLA

Taş, Emre, and Sevil Aykanat. “Approximation Results of Nonlinear Operators via Power Series Statistical Convergence in Modular Space”. Turkish Journal of Mathematics and Computer Science, vol. 18, no. 1, Feb. 2026, pp. 111-9, doi:10.47000/tjmcs.1794000.

Vancouver

1.Emre Taş, Sevil Aykanat. Approximation Results of Nonlinear Operators via Power Series Statistical Convergence in Modular Space. TJMCS. 2026 Feb. 1;18(1):111-9. doi:10.47000/tjmcs.1794000