zbMATH — the first resource for mathematics

Geometry Search for the term Geometry in any field. Queries are case-independent.
Funct* Wildcard queries are specified by * (e.g. functions, functorial, etc.). Otherwise the search is exact.
"Topological group" Phrases (multi-words) should be set in "straight quotation marks".
au: Bourbaki & ti: Algebra Search for author and title. The and-operator & is default and can be omitted.
Chebyshev | Tschebyscheff The or-operator | allows to search for Chebyshev or Tschebyscheff.
"Quasi* map*" py: 1989 The resulting documents have publication year 1989.
so: Eur* J* Mat* Soc* cc: 14 Search for publications in a particular source with a Mathematics Subject Classification code (cc) in 14.
"Partial diff* eq*" ! elliptic The not-operator ! eliminates all results containing the word elliptic.
dt: b & au: Hilbert The document type is set to books; alternatively: j for journal articles, a for book articles.
py: 2000-2015 cc: (94A | 11T) Number ranges are accepted. Terms can be grouped within (parentheses).
la: chinese Find documents in a given language. ISO 639-1 language codes can also be used.

a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
any anywhere an internal document identifier
au author, editor ai internal author identifier
ti title la language
so source ab review, abstract
py publication year rv reviewer
cc MSC code ut uncontrolled term
dt document type (j: journal article; b: book; a: book article)
Fixed point theory in modular function spaces. (English) Zbl 0714.47040
From the text: “The purpose of this paper is to give an outline of a fixed point theory for nonexpansive mappings defined on some subsets of modular function spaces.” The authors use constructive methods to prove fixed point theorems for contractive and nonexpansive mappings on modular spaces. They also study normal structure, uniform convexity and their related properties on modular function spaces, and prove a modular analogue of a fixed point theorem of {\it W. A. Kirk} [Amer. Math. Monthly 72, 1004-1006 (1965; Zbl 0141.324)].
Reviewer: S.L.Singh

47H10Fixed-point theorems for nonlinear operators on topological linear spaces
47H09Mappings defined by “shrinking” properties
46S30Constructive functional analysis
46E30Spaces of measurable functions
46A80Modular topological linear spaces
Full Text: DOI
[1] Alspach, D.: A fixed point free nonexpansive mapping. Proc. am. Math. soc. 82, 423-424 (1981) · Zbl 0468.47036
[2] Brodskii, M. S.; Milman, D. P.: On the center of a convex set. Dokl. acad. Nauk. SSSR 59, 837-840 (1948)
[3] Dunford, N.; Schwartz, J. T.: Linear operators. (1958)
[4] Goebel, K.; Reich, S.: Uniform convexity, hyperbolic geometry, and nonexpansive mappings. (1984) · Zbl 0537.46001
[5] Goebel, K.; Sekowski, T.; Stachura, A.: Uniform convexity of the hyperbolic metric and fixed points of holomorphic mappings in the Hilbert ball. Nonlinear analysis 4, 1011-1021 (1980) · Zbl 0448.47048
[6] Kaminska, A.: On uniform convexity of Orlicz spaces. Indag. math. 44, 27-36 (1982) · Zbl 0489.46025
[7] Khamsi M.A., KOZLOWSKI W.M. & SHUTAO C., Some geometrical properties and fixed point theorems in Orlicz modular spaces (preprint). · Zbl 0752.46011
[8] Khamsi, M. A.: Etude de la propriété du point fixe dans LES espaces de Banach et LES espaces metriques. Thése (1987) · Zbl 0611.46018
[9] Kijima, Y.; Takahashi, W.: A fixed point theorem for nonexpansive mappings in metric spaces. Kodai math. Semin. rep. 21, 326-330 (1969) · Zbl 0188.55401
[10] Kirk, W. A.: A fixed point theorem for mappings which do not increase distances. Am. math. Mon. 72, 1004-1006 (1965) · Zbl 0141.32402
[11] Kirk, W. A.: Fixed point theory for nonexpansive mappings, II. Contemp. math. 18, 121-140 (1983) · Zbl 0511.47037
[12] Kirk, W. A.: Nonexpensive mappings in metric and Banach spaces. Rc. semin. Mat. milano, 133-144 (1981) · Zbl 0519.54029
[13] Kozlowski, W. M.: Notes on modular function spaces I. Commentat. math. 28, 91-104 (1988)
[14] Kozlowski, W. M.: Notes on modular function spaces II. Commentat. math. 28, 105-120 (1988)
[15] Kozlowski, W. M.: Modular function spaces. (1988) · Zbl 0661.46023
[16] Dozo, E. Lami; Turpin, P.: Nonexpansive maps in generalized Orlicz spaces. Studia math. 86, 155-188 (1987) · Zbl 0649.47044
[17] Mairey B., Points fixes des contractions sur un convex fermé de L1, Seminaire d’Analyse Fonctionnelle 80/81, École Polytechnique, Palaiseau.
[18] Musielak, J.: Orlicz spaces and modular spaces. Lecture notes in mathematics 1034 (1983) · Zbl 0557.46020
[19] Peetre, J.: A new approach in interpolation spaces. Studia math. 34, 23-42 (1970) · Zbl 0188.43602
[20] Penot, J. P.: Fixed point theorems without convexity, analyse non convexe. Bull. soc. Math. fr. 60, 129-152 (1979) · Zbl 0454.47044
[21] Pouzet M., JAWHARI E. & MISANE D., Retracts, graphs and ordered sets from the metric point of view, Publication du Dept. de Math., Université Claude Bernard, Lyon, France. · Zbl 0597.54028
[22] Reich, S.: The fixed point property for nonexpansive mappings, II. Am. math. Mon. 87, 292-294 (1980) · Zbl 0443.47057
[23] Rolewicz, S.: Metric linear spaces. (1984) · Zbl 0526.49018
[24] Swaminathan, S.: Normal structure in Banach spaces and its generalizations. Contemp. math. 18, 201-215 (1983) · Zbl 0512.46014
[25] Turett, B.: Rotundity of Orlicz spaces. Indag. math. 38, 462-469 (1976) · Zbl 0388.46022