Turkish Journal of Mathematics
Author ORCID Identifier
SARE YUMRUÇALI: 0009-0004-7184-3299
HARUN KARSLI: 0000-0002-3641-9052
FATMA TAŞDELEN YEŞİLDAL: 0000-0002-6291-1649
Abstract
The aim of the present paper is to introduce generalized Szász–Mirakyan operators. This article studies the property of variation seminorm and some approximation properties of generalized Szász–Mirakyan operators not only in normed spaces but also in variation seminorm. We obtain convergence properties of our operators using of Korovkin’s theorem and the order of convergence by using a classical approach, the second modulus of continuity and Peetre’s K functional. We also give asymptotic formula and the convergence of the derivatives for these operators. We investigate the variation detracting property of generalized Szász–Mirakyan operators. We show the convergence of generalized Szász–Mirakyan operators in variation seminorm and its rate of convergence invariation seminorm.
DOI
10.55730/1300-0098.3624
Keywords
Linear positive operators, generalized Szász-Mirakyan operators, variation detracting property, modulus of continuity, convergence in variation seminorm, Voronovskaya-type theorem
First Page
768
Last Page
783
Publisher
The Scientific and Technological Research Council of Türkiye (TÜBİTAK)
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Recommended Citation
YUMRUÇALI, S, KARSLI, H, & TAŞDELEN YEŞİLDAL, F (2025). Generalized Szász–Mirakyan operators in the variation seminorm. Turkish Journal of Mathematics 49 (6): 768-783. https://doi.org/10.55730/1300-0098.3624
