Two Points and n -th Derivatives Norm Inequalities for Analytic Functions in Banach Algebras

Abstract

UDC 517.5 Let ℬ be a unital Banach algebra, let a ∈ ℬ , G be a convex domain of ℂ with σ ( a ) ⊂ G , let α , β ∈ G , and let f : G → ℂ be analytic on G . By using the analytic functional calculus, we obtain among others the following result:Some examples for the exponential function on Banach algebras are also given.