×
Górnicki, Jarosław

Fixed points of asymptotically regular mappings. (English) Zbl 0806.47049

Math. Slovaca 43, No. 3, 327-336 (1993).
Extending some results from a previous paper [Nonlinear Anal., Theory Methods Appl. 17, No. 2, 153-159 (1991; Zbl 0758.47044)], the author proves some fixed point theorems of asymptotically regular mappings in Lebesgue spaces, Hardy spaces, and Sobolev spaces.
Reviewer: J.Appell (Würzburg)

Cited in 2 Reviews
Cited in 3 Documents

MSC:

47H10 Fixed-point theorems
46E35 Sobolev spaces and other spaces of “smooth” functions, embedding theorems, trace theorems
46E30 Spaces of measurable functions (\(L^p\)-spaces, Orlicz spaces, Köthe function spaces, Lorentz spaces, rearrangement invariant spaces, ideal spaces, etc.)
54H25 Fixed-point and coincidence theorems (topological aspects)

Keywords:

fixed point theorems of asymptotically regular mappings in Lebesgue spaces; Hardy spaces; Sobolev spaces

Citations:

Zbl 0758.47044
Cite Review PDF
Full Text: EuDML

References:

[1] BROWDER F. E., PETRYSHYN V. W.: The solution by iteration of nonlinear functional equations in Banach spaces. Bull. Amer. Math. Soc. 72 (1966), 571-576. · Zbl 0138.08202 · doi:10.1090/S0002-9904-1966-11544-6
[2] BYNUM W. L.: Normal structure coefficients for Banach spaces. Pacific J. Math. 86 (1980), 427-436. · Zbl 0442.46018 · doi:10.2140/pjm.1980.86.427
[3] CASINI E., MALUTA E.: Fixed points of uniformly Lipschitzian mappings in spaces with uniformly normal structure. Nonlinear Anal. 9 (1985), 103-108. · Zbl 0526.47034 · doi:10.1016/0362-546X(85)90055-0
[4] DANEŠ J.: On densifying and related mappings and their applications in nonlinear functional analysis. Theory of Nonlinear Operators. Proc. Summer School, October 1972, GDR, Akademie-Verlag, Berlin, 1974, pp. 15-56.
[5] GOEBEL K., KIRK W. A.: Topics in Metric Fixed Point Theory. Cambridge Stud. Adv. Math. 28, Cambridge University Press, London, 1990. · Zbl 0708.47031
[6] GÓRNICKI J.: Fixed point theorems for asymptotically regular mappings in Lp spaces. Nonlinear Anal. 17 (1991), 153-159. · Zbl 0758.47044 · doi:10.1016/0362-546X(91)90218-P
[7] KRÜPPEL M.: Ein Fixpunktsatz für asymptotisch reguläre Operatoren im Hilbert-Raum. Wiss. Z. Pädagog. Hochsch. ”Liselotte Herrmann” Güstrow Math.-Natur. Fak. 27 (1989), 247-251. · Zbl 0721.47040
[8] LIM T. C.: On some Lp inequalities in best approximation theory. J. Math. Anal. Appl. 154 (1991), 523-528. · Zbl 0744.41015 · doi:10.1016/0022-247X(91)90055-5
[9] LIM T. C., XU H. K., XU Z. B.: An Lp inequality and its applications to fixed point theory and approximation theory. Progress in Approximation Theory, Academic Press, 1991, pp. 609-624.
[10] LIN P. K.: A uniformly asymptotically regular mapping without fixed points. Canad. Math. Bull. 30 (1987), 481-483. · Zbl 0645.47050 · doi:10.4153/CMB-1987-071-6
[11] PICHUGOV S. A.: Jung’s constant of the space Lp. (Russian), Mat. Zametki 43 (1988), 604-614. (Translation: Math. Notes 43 (1988)) · Zbl 0644.46016
[12] PRUS B., SMARZEWSKI R.: Strongly unique best approximations and centers in uniformly convex spaces. J. Math. Anal. Appl. 121 (1987), 10-21. · Zbl 0617.41046 · doi:10.1016/0022-247X(87)90234-4
[13] PRUS S.: On Bynum’s fixed point theorem. Atti Sem. Mat. Fis. Univ. Modena 38 (1990), 535-545. · Zbl 0724.46020
[14] PRUS S.: Some estimates for the normal structure coefficient in Banach spaces. Rend. Circ. Mat. Palermo (2) XL (1991), 128-135. · Zbl 0757.46029 · doi:10.1007/BF02846365
[15] SMARZEWSKI R.: Strongly unique minimization of junctionals in Banach spaces with applications to theory of approximation and fixed points. J. Math. Anal. Appl. 115 (1986), 155-172. · Zbl 0593.49004 · doi:10.1016/0022-247X(86)90030-2
[16] SMARZEWSKI R.: Strongly unique best approximation in Banach spaces II. J. Approx. Theory 51 (1987), 202-217. · Zbl 0657.41022 · doi:10.1016/0021-9045(87)90035-9
[17] SMARZEWSKI R.: Classical and Extended Strong Unicity of Approximation in Banach Spaces. (Polish), Mariae Curie-Sklodowska University, Lublin, 1986.
[18] SMARZEWSKI R.: On the inequality of Bynum and Drew. J. Math. Anal. Appl. 150 (1990), 146-150. · Zbl 0716.46023 · doi:10.1016/0022-247X(90)90201-P
[19] XU H. K.: Inequalities in Banach spaces with applications. Nonlinear Anal. 16 (1991), 1127-1138. · Zbl 0757.46033 · doi:10.1016/0362-546X(91)90200-K
[20] ZALINESCU C.: On uniformly convex function. J. Math. Anal. Appl. 95 (1983), 344-374. · Zbl 0519.49010 · doi:10.1016/0022-247X(83)90112-9
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.