Fixed Points for Mappings on Product Spaces

Abstract

Existence of fixed points for a particular cyclic type of mappings on a finite product of topological spaces is discussed. Existence of fixed points of a particular cyclic type of set valued mappings on a finite product of metric spaces is derived. Fixed points of shift type mappings are studied.

Keywords

• et valued mappings,Hausdorff metrics

References

1. 1. R. Cauty, Solution du probl`eme de point fixe de Schauder, Fund. Math., 170(2001) 231-246 (French)2. T. Dobrowolski, Revisiting Cauty's proof of the Schauder Conjecture, Abstract and applied analysis, 2003:7(2003) 407-433.3. W. A. Kirk, A fixed point theorem for mappings which do not increase distances, Amer. Math. Monthly, 72(1965) 1004-1006. 4. W. A. Kirk, An iteration process for nonexpansive mappings with applications to fixed point theory in product spaces, Proc. Amer. Math. Soc., 107(1989) 411-415.5. W. A. Kirk, P. S. Srinivasan and P. Veeramani, Fixed points for mappings satisfying cyclical contractive conditions, Fixed point theory, 4 (2003), 79-89.W. A. Kirk and C. M. Yanez, Nonexpansive and locally nonexpansive mappings in product spaces, Nonlinear analysis, Theory, Methods and Applications, 12(1988) 719-725.6. D. R. Smart, Fixed point theorems, Cambridge University press, Cambridge, 1974.7. P. Vijayaraju, Fixed point theorems for asymptotically nonexpansive mappings in product spaces, Twiwanese J. Mathematics, 2(1998) 97-105.