We show that the super fixed point property for nonexpansive mappings and for asymptotically nonexpansive mappings in the intermediate sense are equivalent. As a consequence, we obtain fixed point theorems for asymptotically nonexpansive mappings in uniformly nonsquare and uniformly noncreasy Banach spaces. The results are generalized to commuting families of asymptotically nonexpansive mappings.
An explicit representation of the n-fold symmetric tensor product (equipped with a natural topology τ such as the projective, injective or inductive one) of the finite direct sum of locally convex spaces is presented. The formula for gives a direct proof of a recent result of Díaz and Dineen (and generalizes it to other topologies τ) that the n-fold projective symmetric and the n-fold projective “full” tensor product of a locally convex space E are isomorphic if E is isomorphic to its square .
The main purpose of this paper is to introduce the concept of -type fuzzy topological spaces. Further variational principle and Caristi’s fixed point theorem have been extended in the -type fuzzy topological spaces.
Let ⟨X,Y⟩ be a duality pair of M-spaces X,Y of measurable functions from Ω ⊂ ℝ ⁿ into . The paper deals with Y-weak cluster points ϕ̅ of the sequence in X, where is measurable for j ∈ ℕ and is a Carathéodory function. We obtain general sufficient conditions, under which, for some negligible set , the integral exists for and on , where is a measurable-dependent family of Radon probability measures on .