论文信息 - Fixed point theorems for nonexpansive mappings satisfying certain boundary conditions

Fixed point theorems for nonexpansive mappings satisfying certain boundary conditions

Let K be a bounded closed convex subset of a Banach space X with int K /0, and suppose K has the fixed point property with respect to nonexpansive self-mappings (i.e., mappings U: KK such that |U(x) U(y)|| 0. It is shown that if in addition, either (i) T satisfies the Leray-Schauder boundary condition: there exists z e int K such that T(x) z / A(x z) for all x e boundary K, A< 1, or (ii) infIllx T(x)ll: x E K = 0, is satisfied, then T has a fixed point in K.

W. A. Kirk

[1] W. A. Kirk,et al. A FIXED POINT THEOREM FOR k-SET-CONTRACTIONS DEFINED IN A CONE , 1974 .

[2] Simeon Reich,et al. Fixed points of condensing functions , 1973 .

[3] William A. Kirk,et al. Fixed point theorems for set-valued mappings of contractive type , 1972 .

[4] Remarks on condensing and k-set-contractive mappings☆ , 1972 .

[5] R. Nussbaum. The fixed point index for local condensing maps , 1971 .

[6] W. A. Kirk. FIXED POINT THEOREMS FOR NONLINEAR NONEXPANSIVE AND GENERALIZED CONTRACTION MAPPINGS , 1971 .

[7] W. Petryshyn. Structure of the fixed points sets of k-set-contractions , 1971 .

[8] M. Crandall. Differential equations on convex sets , 1970 .

[9] Felix E. Browder,et al. Semicontractive and semiaccretive nonlinear mappings in Banach spaces , 1968 .

[10] George M. Bergman,et al. A FIXED-POINT THEOREM FOR INWARD AND OUTWARD MAPS , 1968 .

[11] Z. Opial. NONEXPANSIVE AND MONOTONE MAPPINGS IN BANACH SPACES. , 1967 .

[12] William A. Kirk,et al. A Fixed Point Theorem for Mappings which do not Increase Distances , 1965 .

[13] F. Browder,et al. NONEXPANSIVE NONLINEAR OPERATORS IN A BANACH SPACE. , 1965, Proceedings of the National Academy of Sciences of the United States of America.

[14] Dietrich Göhde,et al. Zum Prinzip der kontraktiven Abbildung , 1965 .