Fixed points of asymptotically regular semigroups in Banach spaces

Springer Science and Business Media LLC - Tập 46 - Trang 89-118 - 1997
Jarosław Górnicki1
1Department of Mathematics, Technical University of Rzeszów, Rzeszów, Poland

Tóm tắt

In this paper we study in Banach spaces the existence of fixed points of (nonlinear) asymptotically regular semigroups. We establish for these semigroups some fixed point theorems in spaces with weak uniform normal structure, in a Hilbert space, inL p spaces, in Hardy spacesH p and in Sobolev spacesW r.p for 1

Tài liệu tham khảo

Ayerbe J.M., Domínguez Benavides T.,Connections between some Banach space coefficients concerning normal structure, J. Math. Anal. Appl,172 (1993), 53–61. Ayerbe J. M., Xu H. K.,On certain geometric coefficients of Banach spaces relating to the fixed point theory, Panamerican Math J.,3 (1993), 47–59. Barros-Neto J.,An Introduction to the Theory of Distributions, M. Dekker, New York, 1973. Browder E. F., Petryshyn W. V.,The solution of nonlinear functional equations in Banach spaces, Bull. Amer. Math. Soc.,72 (1966), 571–576. Bruck R. E.,Asymptotic behavior of nonexpansive mappings, Contemporray Math.,18 (1983), 1–47. Bynum W. L.,Normal structure coefficients for Banach spaces, Pacific J. Math.,86 (1980), 427–436. Domínguez Benavides T.,Normal structure coefficients of L p(Ω), Proc. Royal Soc. Edinburgh,117A (1991), 299–303. Domínguez Benavides T.,Fixed point theorems for uniformly Lipschitzian mappings and asymptotically regular mappings (preprint, 1995). Domínguez Benavides T., López Acedo G., Xu H. K.Weak uniform normal structure and iterative fixed points of nonexpansive mappings, Coll. Math.,68 (1995), 17–23. Domínguez Benavides T., Xu H. K.,A new geometrical coefficient for Banach spaces and its applications in fixed point theory, Nonlinear Anal.,25 (1995), 311–325. Downing D. J., Turett B.,Some properties of the characteristic of convexity relating to fixed point theory, Pacific J. Math.,104 (1983), 343–350. Dunford N., Schwarz J.,Linear Operators, vol. I, Interscience, New York, 1988. Duren W. L.,Theory of H p Spaces, Academic Press, New York, 1970. Edelstein M.,The construction of an asymptotic center with a fixed point property, Bull. Amer. Math. Soc.,78 (1972), 206–208. Goebel K., Kirk W. A.,Topics in Metric Fixed Point Theory, Cambridge Stud. Adv. Math., 28, Cambridge University Press, London 1990. Górnicki J.,A fixed point theorem for asymptotically regular mappings, Coll. Math.64 (1993), 55–57. Krasnosel’skii M. A., Zabreiko P. P.,Geometrical Methods of Nonlinear Analysis, Springer-Verlag, Berlin, 1984. Lifshitz E. A.,Fixed point theorens for operators in strongly convex spaces (Russian) Voronez. Gos. Univ. Trudy Mat. Fak.,16 (1975), 23–28. Lim T. C.,On some L p inequalities in best approximation theory, J. Math. Anal. Appl.,154 (1991), 523–528. Lim T. C., Xu H. K., Xu Z. B.,L p inequality and its applications to fixed point theory and approximation theory, in: Progress in Approximation Theory (P. Nevai, A. Pinkus, Eds.), Academic Press, (1991), 609–624. Lin P. K., Tan K. K., Xu H. K.,Demiclosedness principle and asymptotic behavior for asymptotically nonexpansive mappings, Nonlinear Anal.,24 (1995), 929–946. Lindnstruss J., Tzfriri L.,Classical Banach Spaces II—Function Spaces, Springer-Verlag, Berlin, 1979. Opial Z.,Weak convergence of the sequence of successive approximations for nonexpansive mappings, Bull. Amer. Math. Soc.,73 (1967), 591–597. Prus B., Smarzewski R.,Strongly unique best approximations and centers in uniformly convex spaces, J. Math. Anal. Appl.,121 (1987), 10–21. Prus S.,Banach spaces with the uniform Opial, property, Nonlinear Anal.,18 (1992), 697–704. Smarzewski R.,Strongly unique best approximation in Banach spaces II, J. Approx. Theory,51 (1987), 202–217. Smarzewski R.,On the inequality of Bynum and Drew, J. Math. Anal. Appl.,150 (1990), 146–150. Webb J. R.L., Zhao W.,On connections between set and ball measures of noncompactness, Bull. London Math. Soc.,22 (1990), 471–477. Xu H. K.,Inequalities in Banach spaces with applications, Nonlinear Anal;16 (1991), 1127–1138. Zhao W.,Geometrical coefficients and measures of noncompactness, Ph. D. Dissertion, University of Glasgow, 1992.