Answering a question of J. Lawson (formulated also earlier, in 1984, by Kamimura and Tang [Theoret. Comput. Sci. 34 (1984) 275–288]) we show that every Polish space admits a bounded complete computational model, as defined below. This results from our construction, in each Polish space 〈X,τ 〉, of a countable family C of non-empty closed subsets of X such that: (cp) each subset of C with the fin...

In general, the Gelfand widths cn(T ) of a map T between Banach spaces X and Y are not equivalent to the Gelfand numbers cn(T ) of T . We show that cn(T ) = cn(T ) (n ∈ N) provided that X and Y are uniformly convex and uniformly smooth, and T has trivial kernel and dense range. c ⃝ 2012 Elsevier Inc. All rights reserved.

We introduce, and study, the regularity normality in ideal bitopological spaces, absent subject literature. Our definitions have advantage of using only open sets two underlying topologies. These new concepts represent generalizations Kelly’s pairwise normality. The extension T0, T1 T2 axioms to these spaces is due Caldas et al.

We prove strong convergence theorem for infinite family of uniformly L−Lipschitzian total quasi-φ-asymptotically nonexpansive multi-valued mappings using a generalized f−projection operator in a real uniformly convex and uniformly smooth Banach space. The result presented in this paper improve and unify important recent results announced by many authors.