Ostrowski`s Type Inequalities for the Complex Integral on Paths

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Constructive Mathematical Analysis
Volume:3 Issue:4
Ostrowski`s Type Inequalities for the Complex Integral on Paths

Ostrowski`s Type Inequalities for the Complex Integral on Paths

Pages : 125-138

View : 92 | Download : 9

Publication Date : 2020-12-01

Article Type : Research Paper

Abstract :In this paper we extend the Ostrowski inequality to the integral with respect to arc-length by providing upper bounds for the quantity |finsert ignore into journalissuearticles values(v);ℓinsert ignore into journalissuearticles values(γ);-∫_{γ}finsert ignore into journalissuearticles values(z);|dz|| under the assumptions that γ is a smooth path parametrized by zinsert ignore into journalissuearticles values(t);, t∈[a,b] with the length ℓinsert ignore into journalissuearticles values(γ);, u=zinsert ignore into journalissuearticles values(a);, v=zinsert ignore into journalissuearticles values(x); with x∈insert ignore into journalissuearticles values(a,b); and w=zinsert ignore into journalissuearticles values(b); while f is holomorphic in G, an open domain and γ⊂G. An application for circular paths is also given. Several applications for circular paths and for some special functions of interest such as the exponential functions are also provided.
Keywords : Complex integral, Ostrowski inequality, Integrals on the paths

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