Zizler [ 34 ] proved that any separable Banach space has an equivalent norm which is uniformly convex in every direction. It is also known that uniformly convex Banach spaces are super-reflexive [ 11 ] which shows that the class of uniformly convex is a lot smaller that the class of uniformly convex in every direction. Let C be a weakly compact nonempty convex subset of X. Assume X is uniformly convex in every direction. Let C be a nonempty weakly compact convex subset of X not reduced to one point.

SIAM J. Matrix Anal.

## SearchWorks Catalog

Nieto, JJ, Rodriguez-Lopez, R: Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations. Order 22 3 , Jachymski, J: The contraction principle for mappings on a metric space with a graph. Springer, New York Cambridge University Press, Cambridge Wiley, New York North-Holland, Amsterdam Lecture Notes in Math. Springer, Berlin Dekker, New York Fixed Point Theory Appl.

Turinici, M: Fixed points for monotone iteratively local contractions. Turinici, M: Ran and Reurings theorems in ordered metric spaces.

## Uniform Convexity Hyperbolic Geometry Nonexpansive by Goebel Kazimierz Reich

Indian Math. Browder, FE: Nonexpansive nonlinear operators in a Banach space. USA 54 , Kirk, WA: A fixed point theorem for mappings which do not increase distances. Reich, S, Shafrir, I: Nonexpansive iterations in hyperbolic spaces. Nonlinear Anal. Busemann, H: Spaces with non-positive curvature. Acta Math. Kirk, WA: Fixed point theory for nonexpansive mappings.

In: Fixed Point Theory. TMA 74 , Khamsi, MA: On metric spaces with uniform normal structure. Ishikawa, S: Fixed points and iteration of a nonexpansive mapping in a Banach space. How to cite item. Email this article Login required.

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Email the author Login required. Keywords Analytic Analytic function Analytic functions Degenerate nonlinear elliptic equations Fibonacci numbers Hadamard product Harmonic mapping Meromorphic functions Opial property Polynomial Polynomials annulus convolution differential subordination individual-based model linear operator natural operator non-strict Opial property subordination superordination weighted Sobolev spaces.

Font Size. Keywords Asymptotic normal structure; Day norm; local uniform convexity; normal structure; Opial property; strict convexity; uniform convexity in every direction.

Full Text: PDF. References Boas, R. Clarkson, J. Hanner, O. Holmes, R. Remember me. O'Regan and D.

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Espnola and P. Lorenzo, Metric fixed point theory on hyperconvex spaces: recent progress, Arab. Goebel and W.

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## Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings | UVA Library | Virgo

Providence, RI, Press, Cambridge, Goebel and S. Goebel, T. Sekowski and A. Stachura, Uniform convexity of the hyperbolic metric and fixed points of holomorphic mappings in the Hilbert ball, Nonlinear Anal.

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### Introduction

Khamsi and A. Khan, Inequalities in metric spaces with applications, Nonlinear Anal. Khan, H. Fukhar-ud-din and M. Khan, An implicit algorithm for two finite families of nonexpansive maps in hyperbolic spaces, Fixed Point Theory Appl. Kirk, A fixed point theorem for mappings which do not increase distances, Amer. Kirk and B. Panyanak, A concept of convergence in geodesic spaces, Nonlinear Anal.

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