On the Problem of Dissipative Perturbations of Nonexpansive Mappings
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Abstract: Some fixed point theorems for mappings of the type-A+T are established,where P is a cone in a Hilbert space,A:P→2P is an accretive mappings and T:P→P is a nonexpansive mappings.In application,the results presented in the paper are used to study the existence problem of solutions for a class of nonlinear integral equations in L2(Ω).
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[1] Gatica J A, Kirk W A. Fixed point theorems for contraction mappings with applications to nonexpansive and pseudo-contractive mappings[J]. Rocky Mountain J Math,1994,4:69-79. [2] Kirk W A,Schonberg R. Some results on pseudo-contractive mappings[J]. Pacific J Math,1977,71:89-100. [3] Morales C. Pseudo-contractive mappings and the Leray-Schauder boundary condition[J]. Comment Math Univ Carolinae,1979,20: 745-756. [4] Reinermann J,Schonberg R. Some Results and Problems in the Fixed Point Theory for Nonexpansive and Pseudo-Contractive Mappings in Hilbert Spaces[M]. S Swaminathaned: Academic Press, 1976. [5] Chen Y Q. The fixed point index for accretive mappings with k-set contraction perturbation in cones[J]. Internat J Math Math Sci,1996, 19(2):287-290. [6] Chen Y Q. On accretive operators in cones of Banach spaces[J]. Nonlinear Anal, TMA,1996,27(10): 1125-1135. [7] Chen Y Q,Cho Y J. On 1-set contractions accretive operators in cones of Banach spaces[J]. J Math Anal Appl,1996,201(3): 966-980. [8] Alspach D E. A fixed point free nonexpansive map[J]. Proc Amer Math Soc,1981,82(3): 423-424. [9] Browder F E. Nonlinear nonexpansive operators in Banach spaces[J]. Proc Nat Acad Sci USA,1965,54: 1041-1044. [10] Browder F E. Nonlinear operators and nonlinear equations of evolution in Banach spaces[J]. Proc Sympos Pure Math,1976,18(2):1023-1027. [11] 张石生. 不动点理论及应用[M]. 重庆:重庆出版社,1984. [12] Isac G. On an Altman type fixed point theorem on convex cones[J]. Rocky Mountain J Math,1995,2: 701-714. -
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