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The purpose of this paper is to establish a general fixed point theorem for mean nonexpansive multivalued mappings defined on weakly compact and convex subsets of Banach spaces with property (D). The main result obtained in this paper significantly extends and improves many of the well-known results in the existing literature. [ABSTRACT FROM AUTHOR]

For Fréchet algebras (A, (pn)) and (B, (qn)), a linear map T : A → B is almost multiplicative with respect to (pn) and (qn), if there exists ε ≥ 0 such that qn (Tab - TaTb) ≤ εpn(a)pn(b), for all n ∊ N, a, b ∈ A, and it is called weakly almost multiplicative with respect to (pn) and (qn), if there exists ε ≥ 0 such that for every k ∈ N, there exists n(k) ∈ N, satisfying the inequality qk(Tab - TaT b)≤ εpn(k)(a)pn(k)(b), for all a, b ∈ A. We investigate the automatic continuity of (weakly) almost multiplicative maps between certain classes of Fréchet algebras, such as Banach algebras and Fréchet Q-algebras. We also obtain some results on the automatic continuity of dense range (weakly) almost multiplicative maps between Fréchet algebras. [ABSTRACT FROM AUTHOR]

We show that the character space of the vector-valued Lipschitz algebra Lipα (X,E) of order α, is homeomorphic to the cartesian product X × ME in the product topology, where X is a compact metric space and E is a unital commutative Banach algebra. We also characterize the form of each character on Lipα (X,E). By appealing to the injective tensor product, we then identify the character space of the vector-valued polynomial Lipschitz algebra LipαP(X,E), generated by the polynomials on the compact space X ⊆ ℂn. It is also shown that LipαP(X,E) is the injective tensor product LipαP(X)⊗εE. Finally, we characterize the form of each character on LipαP (X,E). [ABSTRACT FROM AUTHOR]

We investigate compact composition operators on ceratin Lipschitz spaces of analytic functions on the closed unit disc of the plane. Our approach also leads to some results about composition operators on Zygmund type spaces. [ABSTRACT FROM AUTHOR]