Normalize Edilmiş Hata Fonksiyonunun Kısmi Toplamları Üzerine

Year 2019, , 501 - 504, 15.07.2019

İbrahim Aktaş

https://doi.org/10.17714/gumusfenbil.538739

Abstract

Bu makalenin
temel amacı normalize edilmiş hata fonksiyonunun kısmi toplamlarına oranının
reel kısımları için bazı alt sınırlar belirlemektir. Ek olarak, normalize
edilmiş hata fonksiyonu ve türevinin mutlak değerleri için bazı üst sınırlar da
verilmiştir.

Keywords

Analitik Fonksiyon, Hata Fonksiyonu, Kısmi Toplamlar

On Partial Sums of Normalized Error Function

Abstract

The main purpose of this paper is to determine some
lower bounds for real parts of the quotient of normalized error function and
its partial sum. In addition, the some upper bounds for absolute values of
normalized error function and its derivative are also given.

Keywords

Analytic Function, Error Function, Partial Sums

References

• Abromowitz, M., Stegun, I. A., 1965. Handbook of Mathematical Functions with Formulas, Graphs and Mathematical Tables, Newyork: Dover Publication.
• Aktaş, İ., Partial sums of hyper-Bessel function with applications, Hacettepe Journal of Mathematics and Statistics, (Acccepted).
• Aktaş, İ., Orhan, H., 2016. Partial sums of normalized Dini functions, Journal of Classical Analysis, 9(2), 127-135.
• Aktaş, İ., Orhan, H., 2018. On partial sums of normalized q-Bessel functions, Communication of the Korean Mathematical Society, 33(2), 535-547.
• Alzer, H., 2003. Functional inequalities for the error functions I, Aequationes Mathematicae, 66, 119-127.
• Alzer, H., 2009. Functional inequalities for the error functions II, Aequationes Mathematicae, 78, 113-121.
• Alzer, H., 2010. Error function inequalities, Advances in Computational Mathematics, 33, 349-379.
• Çağlar, M., Deniz, E., 2015. Partial sums of the normalized Lommel functions. Mathematical Inequalities and Applications, 18(3), 1189-1199.
• Çağlar, M., Orhan, H., 2017. On neighborhood and partial sums promlem for generalized Sakaguchi type functions. Analele Stiintifice Ale Universitatii Al I Cuza Din Iasi-Serie Noua-Matematica, Tomul LXIII, f. 1, 17-28.
• Kreyszig, E., Todd, J., 1959a. The radius of univalence of the error function, Numerische Mathematik, 1, 78-89.
• Kreyszig, E., Todd, J., 1959b. On the Radius of univalence of the function exp⁡〖z^2 〗 ∫_0^z▒exp⁡〖(-t^2)dt〗 , Pasifik Journal of Mathematics, 9(1), 123-127.
• Ramachandran, C., Vanitha, L., Kanas, S., 2018. Certain results on q- starlike and q-convex error functions, Mathematica Slovaca, 68(2), 361-368.
• Silverman, H., 1997. Partial sums of starlike and convex functions, Journal of Mathematical Analysis and Applications, 209, 221-227.
• Silvia, EM., 1985. On partial sums of convex functions of order α, Houston Journal of Mathematics, 11, 397-404.