In this paper we extend the trapezoid inequality to the complex integral by providing upper bounds for the quantity |(v−u)f(u)+(w−v)f(w)−∫γf(z)dz||(v−u)f(u)+(w−v)f(w)−∫γf(z)dz| under the assumptions that $γ$ is a smooth path parametrized by z(t),t∈[a,b],u=z(a),v=z(x)z(t),t∈[a,b],u=z(a),v=z(x) with x∈(a,b)x∈(a,b) and w=z(b)w=z(b) while ff is holomorphic in GG, an open domain and γ∈Gγ∈G. An application for circular paths is also given.
Complex integral continuous functions holomorphic functions trapezoid inequality
Birincil Dil | İngilizce |
---|---|
Konular | Matematik |
Bölüm | Research Article |
Yazarlar | |
Yayımlanma Tarihi | 31 Aralık 2021 |
Gönderilme Tarihi | 23 Eylül 2020 |
Kabul Tarihi | 17 Nisan 2021 |
Yayımlandığı Sayı | Yıl 2021 Cilt: 70 Sayı: 2 |
Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.
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