Article

 Title: Fixed point theorems for nonexpansive operators with dissipative perturbations in cones  (English) Author: Chang, S. S. Author: Chen, Y. Q. Author: Cho, Y. J. Author: Lee, B. S. Language: English Journal: Commentationes Mathematicae Universitatis Carolinae ISSN: 0010-2628 (print) ISSN: 1213-7243 (online) Volume: 39 Issue: 1 Year: 1998 Pages: 49-54 . Category: math . Summary: Let $P$ be a cone in a Hilbert space $H$, $A: P\rightarrow 2^P$ be an accretive mapping (equivalently, $-A$ be a dissipative mapping) and $T:P\rightarrow P$ be a nonexpansive mapping. In this paper, some fixed point theorems for mappings of the type $-A+T$ are established. As an application, we utilize the results presented in this paper to study the existence problem of solutions for some kind of nonlinear integral equations in $L^2(\Omega)$. Keyword: nonexpansive mapping Keyword: accretive mapping Keyword: fixed point theorem Keyword: nonlinear integral equations MSC: 45G10 MSC: 45H10 MSC: 47H06 MSC: 47H09 MSC: 47H10 MSC: 47H15 idZBL: Zbl 0937.47053 idMR: MR1622324 . Date available: 2009-01-08T18:38:44Z Last updated: 2012-04-30 Stable URL: http://hdl.handle.net/10338.dmlcz/118983 . Reference: [1] Alspach D.E.: A fixed point free nonexpansive map.Proc. Amer. Math. Soc. 82 (1981), 423-424. Zbl 0468.47036, MR 0612733 Reference: [2] F. E. Browder F.E.: Nonlinear nonexpansive operators in Banach spaces.Proc. Nat. Acad. Sci. U.S.A 54 (1965), 1041-1044. MR 0187120 Reference: [3] Browder F.E.: Nonlinear Operators and Nonlinear Equations of Evolution in Banach Spaces.Proc. Symp. Pure Math. Vol. 18, Part 2 (1976). Zbl 0327.47022, MR 0405188 Reference: [4] Chang S.S.: Fixed Point Theory with Applications.Chongqing Publishing House, Chongqing (1984). Reference: [5] Chen Y.Q.: The fixed point index for accretive mappings with $k$-set contraction perturbation in cones.Internat. J. Math. and Math. Sci. 2 (1996), 287-290. MR 1375990 Reference: [6] Chen Y.Q.: On accretive operators in cones of Banach spaces.Nonlinear Anal. TMA 27 (1996), 1125-1135. Zbl 0883.47057, MR 1407451 Reference: [7] Chen Y.Q., Cho Y.J.: On $1$-set contraction perturbations of accretive operators in cones of Banach spaces.J. Math. Anal. Appl. 201 (1996), 966-980. Zbl 0864.47027, MR 1400574 Reference: [8] Gatica J.A., Kirk W.A.: Fixed point theorems for contraction mappings with applications to nonexpansive and pseudo-contractive mappings.Rocky Mountain J. Math. 4 (1994), 69-79. MR 0331136 Reference: [9] Isac G.: On an Altman type fixed point theorem on convex cones.Rocky Mountain J. Math. 2 (1995), 701-714. Zbl 0868.47035, MR 1336557 Reference: [10] Kirk W.A., Schonberg R.: Some results on pseudo-contractive mappings.Pacific J. Math. 71 (1977), 89-100. MR 0487615 Reference: [11] Morales C.: Pseudo-contractive mappings and the Leray-Schauder boundary condition.Comment. Math. Univ. Carolinae 20 (1979), 745-756. Zbl 0429.47021, MR 0555187 Reference: [12] Reinermann J., Schonberg R.: Some results and problems in the fixed point theory for nonexpansive and pseudo-contractive mappings in Hilbert spaces.Academic Press, S. Swaminathan ed. (1976). .

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