A classical problem in functional analysis has been to give a geometric characterization of reflexivity for a Banach space. The first result of this type was D.P. Milman’s [Mil] and B.J. Pettis’ [P] theorem that a uniformly convex space is reflexive. While perhaps considered elementary today it illustrated how a geometric property can be responsible for a topological property. Of course a Banac...

This paper provides a fixed point theorem for asymptotically nonexpansive mappings in uniformly convex hyperbolic spaces as well as new effective results on the Krasnoselski-Mann iterations of such mappings. The latter were found using methods from logic and the paper continues a case study in the general program of extracting effective data from prima-facie ineffective proofs in the fixed poin...

In this paper, we present some fixed point results for a generalized class of nonexpansive mappings in the framework uniformly convex hyperbolic space and also propose new iterative scheme approximating spaces. Furthermore, establish basic properties strong $\triangle$-convergence theorems these Finally, an application to nonlinear integral equation also, numerical example illustrate our main r...

In [6], the second author proved general metatheorems for the extraction of effective uniform bounds from ineffective existence proofs in functional analysis, more precisely from proofs in classical analysis A(:= weakly extensional Peano arithmetic WE-PA in all finite types + quantitifer-free choice + the axiom schema of dependent choice DC) extended with (variants of) abstract bounded metric s...