Keywords: fixed point; minimal displacement; defect of fixed point; best almost-fixed point
@article{ARM_2002_38_4_a3,
author = {Ban, A. I. and Gal, S. G.},
title = {On the minimal displacement of points under mappings},
journal = {Archivum mathematicum},
pages = {273--284},
year = {2002},
volume = {38},
number = {4},
mrnumber = {1942657},
zbl = {1068.47069},
language = {en},
url = {http://geodesic.mathdoc.fr/item/ARM_2002_38_4_a3/}
}
Ban, A. I.; Gal, S. G. On the minimal displacement of points under mappings. Archivum mathematicum, Tome 38 (2002) no. 4, pp. 273-284. http://geodesic.mathdoc.fr/item/ARM_2002_38_4_a3/
[1] Barbu V.: Mathematical methods in optimization of differential systems. (in Romanian), Ed. Academiei, Bucharest, 1989. | MR | Zbl
[2] Ekeland I.: On the variational principle. J. Math. Anal. Appl. 47 (1974), 324–353. | MR | Zbl
[3] Ekeland I.: Nonconvex minimization problems. Bull. Amer. Math. Soc. 1 (1979), 443–474. | MR | Zbl
[4] Engl H. W.: Weak convergence of asymptotically regular sequences for nonexpansive mappings and connections with certain Chebyshef-centers. Nonlinear Anal. 1(5) (1977), 495–501. | MR | Zbl
[5] Ky Fan: Extensions of two fixed point theorems of F.E. Browder. Math. Z. 112 (1969), 234–240. | MR | Zbl
[6] Franchetti C.: Lipschitz maps and the geometry of the unit ball in normed spaces. Arch. Math. 46 (1986), 76–84. | MR | Zbl
[7] Furi M., Martelli M.: On the minimal displacement of points under alpha-Lipschitz maps in normed spaces. Bull. Un. Mat. Ital. 9 (1974), 791–799. | MR | Zbl
[8] Goebel K.: On the minimal displacement of points under lipschitzian mappings. Pacific J. Math. 48 (1973), 151–163. | MR | Zbl
[9] Goebel K., Kirk W. A.: Topics in Metric Fixed Point Theory. Cambridge University Press, Cambridge, 1990. | MR | Zbl
[10] Guay M. D., Singh K. L.: Fixed points of asymptotically regular mappings. Math. Vesnik 35 (1983), 101–106. | MR | Zbl
[11] Kelley J. L.: General Topology. Van Nostrand, New York, 1964. | MR
[12] Rădulescu S., Rădulescu M.: Theorems and Problems in Analysis. (in Romanian), Ed. Didactică şi Pedagogică, Bucharest, 1982.
[13] Reich S.: Minimal displacement of points under weakly inward pseudo-lipschitzian mappings. I, Atti. Acad. Naz. Linzei Rend. U. Sci. Fis. Mat. Natur. 59 (1975), 40–44. | MR
[14] Reich S.: Minimal displacement of points under weakly inward pseudo-lipschitzian mappings. II, Atti. Acad. Naz. Linzei Rend. U. Sci. Fis. Mat. Natur. 60 (1976), 95–96. | MR | Zbl
[15] Rhoades B. E., Sessa S., Khan M. S., Swaleh M.: On fixed points of asymptotically regular mappings. J. Austral. Math. Soc. (Series A) 43 (1987), 328–346. | MR | Zbl
[16] Rus I. A.: Principles and Applications of Fixed Point Theory. (in Romanian), Ed. Dacia, Cluj-Napoca, 1979.