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Topological Methods in Nonlinear Functional Analysis
Edited by: S. P. Singh, S. Thomeier, and B. Watson
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Contemporary Mathematics
1983; 218 pp; softcover
Volume: 21
ISBN-10: 0-8218-5023-7
ISBN-13: 978-0-8218-5023-7
List Price: US$40 Member Price: US$32
Order Code: CONM/21

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 Krasnosel'skiĭ'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.

• M. Altman -- Contractors and fixed points
• F. E. Browder -- The degree of mapping, and its generalizations
• R. F. Brown -- Multiple fixed points of compact maps on wedgelike ANRS in Banach spaces
• E. R. Fadell and S. Husseini -- The Nielsen numbers on surfaces
• G. Fournier -- A good class of eventually condensing maps
• K. Goebel and W. A. Kirk -- Iteration process for nonexpansive mappings
• M. von Golitschek and E. W. Cheney -- The best approximation of bivariate functions of separable functions
• R. Guzzardi -- Positive solutions of operator equations in the nondifferentiable case
• D. S. Jaggi -- On fixed points of nonexpansive mappings
• M. Martelli -- Large oscillations of forced nonlinear differential equations
• S. A. Naimpally, K. L. Singh, and J. H. W. Whitfield -- Fixed points and sequences of iterates in locally convex spaces
• P. L. Papini -- Fixed points theorems and Jung constant in Banach spaces
• W. V. Petryshyn -- Some results on multiple positive fixed points of multivalued condensing maps
• S. Reich -- Some problems and results in fixed point theory
• B. E. Rhoades -- Contractive definitions revisited
• H. Schirmer -- Fixed points, antipodal points and coincidences of n-acyclic multifunctions
• V. M. Sehgal, S. P. Singh, and B. Watson -- A coincidence theorem for topological vector spaces
• V. M. Sehgal and C. Waters -- Some random fixed point theorems