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Fixed point theorems for generalized nonexpansive mappings

Published online by Cambridge University Press:  09 April 2009

Chi Song Wong
Chi Song Wong
Affiliation:
Summer Research Institute, Department of Mathematics, University of Alberta, Edmonton, Alberta, Canada
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Let S, T be self-mappings on a (non-empty) complete metric space (X, d). Let ai, i = 1, 2, …, 5, be non-negative real numbers such that < 1 and for any x, y in X,

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 18 , Issue 3 , November 1974 , pp. 265 - 276
Copyright
Copyright © Australian Mathematical Society 1974

References

[1]Belluce, L. P. and Kirk, W. A., ‘Fixed-point theorems for families of contraction mappings’, Pacific J. Math. 18 (1966), 213–217.CrossRefGoogle Scholar
[2]Belluce, L. P. and Kirk, W. A., ‘Nonexpansive mappings and fixed-points in Banach spaces’, Illinois J. Math. 11 (1967), 471–479.CrossRefGoogle Scholar
[3]Belluce, L. P. and Kirk, W. A., ‘Fixed point theorems for certain classes of nonexpansive mappings’, Proc. Amer. Math. Soc. 20 (1969), 141–146.CrossRefGoogle Scholar
[4]Belluce, L. P. and Kirk, W. A., ‘Some fixed point theorems in a metric and Banach space’, Canad. Math. Bull. 12 (1969), 481–489.CrossRefGoogle Scholar
[5]Boyd, D. W. and Wong, J. S. W., ‘On nonlinear contractions’, Proc. Amer. Math. Soc. 20 (1969), 458–464.CrossRefGoogle Scholar
[6]Brodskii, M. S. and Milman, D. P., ‘On the center of a convex set’, Dokl. Akad. Nauk. SSSR (N.S.) 59 (1948), 837–840.Google Scholar
[7]Browder, F. E., ‘Nonexpansive nonlinear operators in a Banach space’, Proc. Nat. Acad. Sci. U.S.A. (1966), 1041–1044.Google Scholar
[8]Clarkson, J. A., ‘Uniformly convex spaces’, Trans. Amer. Math. Soc. 40 (1936), 396–414.CrossRefGoogle Scholar
[9]Dotson, W. G. Jr, ‘Fixed points of quasi-nonexpansive mappings’, J. Austral. Math. Soc. 13 (1972), 167–170.CrossRefGoogle Scholar
[10]Edelstein, M., ‘The construction of an asymptotic center with a fixed point preoperty’, Bull. Amer. Math. Soc. 18 (1972), 206–208.CrossRefGoogle Scholar
[11]Floret, Klaus, ‘Eine Bermekung über a priori-Fixpunkte nicht-expansiver Abbildungen’, Manuscripta math. 6 (1972), 321–326.CrossRefGoogle Scholar
[12]Göhde, Von Dretrich, ‘Zum prinzip der Konstraktiven Abbildung’, Math. Nachr. 30 (1965), 251–258.CrossRefGoogle Scholar
[13]Hardy, G. and Rogers, T., ‘A generalization of a fixed point theorem of Reich’, Canad. Math. Bull. 16 (1973), 201–206.CrossRefGoogle Scholar
[14]Holmes, R. D. and Lau, Anthony T., ‘Non-expansive actions of topological semigroups’ (to appear in J. London Math. Soc.).Google Scholar
[15]Kannan, R.. ‘Some results on fixed points II’, Amer. Math. Monthly 76 (1969), 405–408.Google Scholar
[16]Kijima, Yōichi and Takahashi, Wataru, ‘A fixed point theorem for nonexpansive mappings in metric space’, Kodai Math. Sem. Rep. 21 (1969), 326–330.CrossRefGoogle Scholar
[17]Kirk, W. A., ‘A fixed point theorem for mappings which do not increase distance’, Amer. Math. Monthly 72 (1965), 1004–1007.CrossRefGoogle Scholar
[18]Kirk, W. A., ‘On mappings with diminishing orbital diameters’, J.London Math. Soc. 44 (1969), 107–111.CrossRefGoogle Scholar
[19]Kirk, W. A., ‘Fixed point theorems for nonexpansive mappings’, Proc. Sympos. Pure Math. 18 Amer. Math. Soc., Providence, R.I. (1970), 162–168.Google Scholar
[20]Kirk, W. A. and Royalty, W. D., ‘Fixed point theorems for certain nonexpansive mappings’. Illinois J. Math. 15 (1971), 656–663.CrossRefGoogle Scholar
[21]Lau, Anthony To-Ming, ‘Invariant means on almost periodic functions and fixed point properties’, (to appear in Rocky Mountain J. Math.).Google Scholar
[22]Marr, Ralph De, ‘Common fixed-points for commuting contraction mappings’, Pacific J. Math. 13 (1963), 1139–1141.Google Scholar
[23]Mitchell, Theodore, ‘Fixed points of reversible semigroups of nonexpansive mappings’, Kodai Math. Sem. Rep. 22 (1970), 322–323.CrossRefGoogle Scholar
[24]Pettis, B. J., ‘A proof that every uniformly convex space is reflexive’, Duke Math. J. 5 (1939), 249–253.CrossRefGoogle Scholar
[25]Rakotch, E. A., ‘A note on contractive mappings’, Proc. Amer. Math. Soc. 13 (1962), 459–465.CrossRefGoogle Scholar
[26]Reich, Simon, ‘Some remarks concerning contraction mappings’, Canad. Math. Bull. 14 (1971), 121–124.CrossRefGoogle Scholar
[27]Srivastava, Pramila and Gupta, Vijay Kummer, ‘A note on common fixed points’, Yokohama Math. J. 19 (1971), 91–95.Google Scholar
[28]Takahashi, Wataru, ‘Fixed point theorem for amenable semigroups of nonexpansive mappings’, Kodai Math. Sem. Rep. 21 (1969), 383–386.CrossRefGoogle Scholar
[29]Takahashi, Watar, ‘A convexity in metric space and nonexpansive mappings’, I, Kodai Math. Sem. Rep. 22 (1970), 142–149.Google Scholar
[30]Wong, Chi Song, ‘Common fixed points of two mappings’, Pacific J. Math. 48 (1973), 299–312.CrossRefGoogle Scholar
[31]Wong, Chi Song, ‘Generalized contractions and fixed point theorems’, Proc. Amer. Math. Soc. 42 (1974), 409–417.CrossRefGoogle Scholar