METRIC FIXED POINT THEORY: OLD PROBLEMS AND NEW DIRECTIONS

This is a brief review of some of the things, both past and present, which have motivated the writer’s interest in metric fixed point theory.

[1]  W. A. Kirk.  Hyperconvexity of R-trees , 2007 .

[2]  William A. Kirk,et al.  Fixed point theorems in R-trees with applications to graph theory , 2006 .

[3]  P. Lin,et al.  Fixed points of isometries on weakly compact convex sets , 2003 .

[4]  Ulrich Kohlenbach,et al.  Some logical metatheorems with applications in functional analysis , 2003 .

[5]  Mohamed A. Khamsi,et al.  Introduction to hyperconvex spaces , 2001 .

[6]  Victor Chepoi,et al.  Graphs of Some CAT(0) Complexes , 2000, Adv. Appl. Math..

[7]  M. Bridson,et al.  Metric Spaces of Non-Positive Curvature , 1999 .

[8]  M. Bestvina.  Real trees in topology, geometry, and group theory , 1997, math/9712210.

[9]  Juan Vicente Llinares,et al.  A fixed point theorem without convexity , 1997 .

[10]  A. Dress,et al.  The Real Tree , 1996 .

[11]  Van de M. L. J. Vel.  Theory of convex structures , 1993 .

[12]  I. Shafrir.  The approximate fixed point property in Banach and hyperbolic spaces , 1990 .

[13]  Itai Shafrir,et al.  Nonexpansive iterations in hyperbolic spaces , 1990 .

[14]  R. Sine.  Hyperconvexity and approximate fixed points , 1989 .

[15]  J. Baillon.  Nonexpansive mappings and hyperconvex spaces , 1988 .

[16]  Hans-Jürgen Bandelt,et al.  A fixed cube theorem for median graphs , 1987, Discret. Math..

[17]  Alain Quilliot.  On the Helly Property Working as a Compactness Criterion on Graphs , 1985, J. Comb. Theory, Ser. A.

[18]  S. Reich,et al.  Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings , 1984 .

[19]  S. Singh,et al.  Topological Methods in Nonlinear Functional Analysis , 1983 .

[20]  W. A. Kirk,et al.  Iteration processes for nonexpansive mappings , 1983 .

[21]  W. A. Kirk.  Krasnoselskii's iteration process in hyperbolic space , 1982 .

[22]  K. Goebel,et al.  Uniform convexity of the hyperbolic metric and fixed points of holomorphic mappings in the Hilbert ball , 1980 .

[23]  W. Ray,et al.  The fixed point property and unbounded sets in Hilbert space , 1980 .

[24]  Richard J. Nowakowski,et al.  Fixed-edge theorem for graphs with loops , 1979, J. Graph Theory.

[25]  B. Fisher.  A Common Fixed Point Theorem for Commuting Mappings , 1979 .

[26]  Teck-Cheong Lim,et al.  A fixed point theorem for families on nonexpansive mappings. , 1974 .

[27]  Ronald E. Bruck.  A COMMON FIXED POINT THEOREM FOR A COMMUTING FAMILY OF NONEXPANSIVE MAPPINGS , 1974 .

[28]  Wataru Takahashi,et al.  A convexity in metric space and nonexpansive mappings, I , 1970 .

[29]  William M. Boyce,et al.  Commuting functions with no common fixed point , 1969 .

[30]  G. Jungck.  Commuting Mappings and Common Fixed Points , 1966 .

[31]  W. A. Kirk,et al.  Fixed-point theorems for families of contraction mappings. , 1966 .

[32]  Common periodic points of commuting functions. , 1965 .

[33]  J. Maxfield,et al.  Common Fixed Points of Commuting Continuous Functions on the Unit Interval , 1965 .

[34]  R. Demarr,et al.  Common fixed points for commuting contraction mappings , 1963 .

[35]  G. S. Young.  Fixed-point theorems for arcwise connected continua , 1960 .

[36]  N. Aronszajn,et al.  EXTENSION OF UNIFORMLY CONTINUOUS TRANSFORMATIONS AND HYPERCONVEX METRIC SPACES , 1956 .

[37]  G. S. Young.  The Introduction of Local Connectivity by Change of Topology , 1946 .

[38]  Shizuo Kakutani,et al.  Two fixed-point theorems concerning bicompact convex sets , 1938 .

[39]  M. Fabian,et al.  Uniform Convexity of , 2022 .