Electronic ISBN:  9780821876077 
Product Code:  CONM/21.E 
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Book DetailsContemporary MathematicsVolume: 21; 1983; 218 ppMSC: Primary 47; Secondary 54;
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 quasinonexpansive 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 wellknown 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.

Table of Contents

Articles

Mieczyslaw Altman  Contractors and fixed points [ MR 729502 ]

Felix E. Browder  The degree of mapping, and its generalizations [ MR 729503 ]

Robert F. Brown  Multiple fixed points of compact maps on wedgelike ANRs in Banach spaces [ MR 729504 ]

Edward Fadell and Sufian Husseini  The Nielsen number on surfaces [ MR 729505 ]

Gilles Fournier  A good class of eventually condensing maps [ MR 729506 ]

Kazimierz Goebel and W. A. Kirk  Iteration processes for nonexpansive mappings [ MR 729507 ]

M. von Golitschek and E. W. Cheney  The best approximation of bivariate functions by separable functions [ MR 729508 ]

Renato Guzzardi  Positive solutions of operator equations in the nondifferentiable case [ MR 729509 ]

D. S. Jaggi  On fixed points of nonexpansive mappings [ MR 729510 ]

Mario Martelli  Large oscillations of forced nonlinear differential equations [ MR 729511 ]

S. A. Naimpally, K. L. Singh and J. H. M. Whitfield  Fixed points and sequences of iterates in locally convex spaces [ MR 729512 ]

P. L. Papini  Fixed point theorems and Jung constant in Banach spaces [ MR 729513 ]

W. V. Petryshyn  Some results on multiple positive fixed points of multivalued condensing maps [ MR 729514 ]

Simeon Reich  Some problems and results in fixed point theory [ MR 729515 ]

B. E. Rhoades  Contractive definitions revisited [ MR 729516 ]

Helga Schirmer  Fixed points, antipodal points and coincidences of $n$acyclic valued multifunctions [ MR 729517 ]

V. M. Sehgal, S. P. Singh and B. Watson  A coincidence theorem for topological vector spaces [ MR 729518 ]

V. M. Sehgal and Charlie Waters  Some random fixed point theorems [ MR 729519 ]


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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 quasinonexpansive 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 wellknown 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.

Articles

Mieczyslaw Altman  Contractors and fixed points [ MR 729502 ]

Felix E. Browder  The degree of mapping, and its generalizations [ MR 729503 ]

Robert F. Brown  Multiple fixed points of compact maps on wedgelike ANRs in Banach spaces [ MR 729504 ]

Edward Fadell and Sufian Husseini  The Nielsen number on surfaces [ MR 729505 ]

Gilles Fournier  A good class of eventually condensing maps [ MR 729506 ]

Kazimierz Goebel and W. A. Kirk  Iteration processes for nonexpansive mappings [ MR 729507 ]

M. von Golitschek and E. W. Cheney  The best approximation of bivariate functions by separable functions [ MR 729508 ]

Renato Guzzardi  Positive solutions of operator equations in the nondifferentiable case [ MR 729509 ]

D. S. Jaggi  On fixed points of nonexpansive mappings [ MR 729510 ]

Mario Martelli  Large oscillations of forced nonlinear differential equations [ MR 729511 ]

S. A. Naimpally, K. L. Singh and J. H. M. Whitfield  Fixed points and sequences of iterates in locally convex spaces [ MR 729512 ]

P. L. Papini  Fixed point theorems and Jung constant in Banach spaces [ MR 729513 ]

W. V. Petryshyn  Some results on multiple positive fixed points of multivalued condensing maps [ MR 729514 ]

Simeon Reich  Some problems and results in fixed point theory [ MR 729515 ]

B. E. Rhoades  Contractive definitions revisited [ MR 729516 ]

Helga Schirmer  Fixed points, antipodal points and coincidences of $n$acyclic valued multifunctions [ MR 729517 ]

V. M. Sehgal, S. P. Singh and B. Watson  A coincidence theorem for topological vector spaces [ MR 729518 ]

V. M. Sehgal and Charlie Waters  Some random fixed point theorems [ MR 729519 ]