Cilt:70 Sayı:02 (2021)

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https://dspace.ankara.edu.tr/handle/20.500.12575/86251

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Browsing Cilt:70 Sayı:02 (2021) by Subject "Complex integral, continuous functions, holomorphic functions, trapezoid inequality"

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    An extension of trapezoid inequality to the complex integral
    (Ankara Universitesi, 2021) Dragomir, Sever; Other; Other
    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 ) − ∫ γ f ( z ) d z | under the assumptions that γ is a smooth path parametrized by z ( t ) , t ∈ [ a , b ] , u = z ( a ) , v = z ( x ) with x ∈ ( a , b ) and w = z ( b ) while f is holomorphic in G , an open domain and γ ∈ G . An application for circular paths is also given.