TY  - JOUR
T1  - On approximation properties by exponential type of Bernstein-Stancu Operators
TT  - Üstel tip Bernstein-Stancu Operatörlerinin yaklaşım özellikleri üzerine
AU  - Acar, Ecem
PY  - 2025
DA  - January
Y2  - 2024
DO  - 10.25092/baunfbed.1553994
JF  - Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi
JO  - BAUN Fen. Bil. Enst. Dergisi
PB  - Balıkesir Üniversitesi
WT  - DergiPark
SN  - 1301-7985
SP  - 315
EP  - 323
VL  - 27
IS  - 1
LA  - en
AB  - In the paper, we introduced a generalization of Bernstein-Stancu-Kantorovich operators that reproduces exponential functions. For appropriate function spaces, both the uniform and L^p convergence have been established. We proved that the new operators satisfy the Korovkin tests with the exponential functions and calculated the operators’ analytical expressions evaluated on various powers of e ^μxwhich is necessary to get the uniform convergence conclusion using the well-known Korovkin Theorem. Consequently, the convergence theorem for the new operators, which transfer the weighted space  L_μ^p ([0,1]) to itself, has been established. Additionally, using the usual modulus of continuity of the estimated function in the continuous case, we provide quantitative estimates for the approximation error.
KW  - Bernstein-Kantorovich operators
KW  - Exponential polynomials
KW  - Modulus of continuity.
N2  - Bu çalışmada üstel fonksiyonları yeniden üreten Bernstein-Stancu-Kantorovich operatörlerinin bir genellemesi sunulmuştur. Uygun fonksiyon uzayları için hem düzgün hem de L^p yakınsaması kurulmuştur. Yeni operatörlerin üstel fonksiyonu sağladığını kanıtladık ve iyi bilinen Korovkin Teoremini kullanarak düzgün yakınsaklık sonucunu elde etmek için gerekli olan e ^μxin çeşitli kuvvetlerine göre değerlendirilen operatörlerin analitik ifadelerini hesapladık. Sonuç olarak L_μ^p ([0,1]) ağırlıklı uzayını kendisine aktaran yeni operatörler için yakınsama teoremi kurulmuştur. Ek olarak, sürekli durumda tahmin edilen fonksiyonun olağan süreklilik modülünü kullanarak, yaklaşık hatası için niceliksel tahminler verilmiştir.
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UR  - https://doi.org/10.25092/baunfbed.1553994
L1  - https://dergipark.org.tr/tr/download/article-file/4231575
ER  -