This volume contains the proceedings of the special session on Fixed Point Theory and Applications held during the Summer Meeting of the American Mathematical Society at the University of Toronto, August 21-26, 1982. The theory of contractors and contractor directions is developed and used to obtain the existence theory under rather weak conditions. Theorems on the existence of fixed points of nonexpansive mappings and the convergence of the sequence of iterates of nonexpansive and quasi-nonexpansive mappings are given. Degree of mapping and its generalizations are given in detail. A class of eventually condensing mappings is studied and multivalued condensing mappings with multiple fixed points are also given.Topological fixed points, including the study of the Nielsen number of a selfmap on a compact surface, extensions of a well-known result of Krasnoselskii's Compression of a Cone Theorem, are given. Also, fixed points, antipodal points, and coincidences of multifunctions are discussed. Several results with applications in the field of partial differential equations are given. Application of fixed point theory in the area of Approximation Theory is also illustrated.
Contractors and fixed points by M. Altman The degree of mapping, and its generalizations by F. E. Browder Multiple fixed points of compact maps on wedgelike ANRS in Banach spaces by R. F. Brown The Nielsen numbers on surfaces by E. R. Fadell and S. Husseini A good class of eventually condensing maps by G. Fournier Iteration process for nonexpansive mappings by K. Goebel and W. A. Kirk The best approximation of bivariate functions of separable functions by M. von Golitschek and E. W. Cheney Positive solutions of operator equations in the nondifferentiable case by R. Guzzardi On fixed points of nonexpansive mappings by D. S. Jaggi Large oscillations of forced nonlinear differential equations by M. Martelli Fixed points and sequences of iterates in locally convex spaces by S. A. Naimpally, K. L. Singh, and J. H. W. Whitfield Fixed points theorems and Jung constant in Banach spaces by P. L. Papini Some results on multiple positive fixed points of multivalued condensing maps by W. V. Petryshyn Some problems and results in fixed point theory by S. Reich Contractive definitions revisited by B. E. Rhoades Fixed points, antipodal points and coincidences of n-acyclic multifunctions by H. Schirmer A coincidence theorem for topological vector spaces by V. M. Sehgal, S. P. Singh, and B. Watson Some random fixed point theorems by V. M. Sehgal and C. Waters.