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)
Best proximity point theorems for cyclic orbital Meir-Keeler contraction maps. (English) Zbl 1206.54047
Summary: We introduce a notion of cyclic orbital Meir-Keeler contraction and give sufficient conditions for the existence of fixed points and best proximity points of such a map. Our main result is a generalization of a best proximity point result due to {\it C. Di Bari, T. Suzuki} and {\it C. Vetro} [Nonlinear Anal., Theory Methods Appl. 69, No. 11, A, 3790--3794 (2008; Zbl 1169.54021)].

54H25Fixed-point and coincidence theorems in topological spaces
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
Full Text: DOI
[1] Kirk, W. A.; Srinivasan, P. S.; Veeramani, P.: Fixed points for mappings satisfying cyclical contractive conditions, Fixed point theory 4, 79-89 (2003) · Zbl 1052.54032
[2] Eldred, A. A.; Veeramani, P.: Existence and convergence of best proximity points, J. math. Anal. appl. 323, 1001-1006 (2006) · Zbl 1105.54021 · doi:10.1016/j.jmaa.2005.10.081
[3] Di Bari, C.; Suzuki, T.; Vetro, C.: Best proximity points for cyclic Meir--Keeler contractions, Nonlinear anal. 69, 3790-3794 (2008) · Zbl 1169.54021 · doi:10.1016/j.na.2007.10.014
[4] Meir, A.; Keeler, E.: A theorem on contraction mappings, J. math. Anal. appl. 28, 326-329 (1969) · Zbl 0194.44904 · doi:10.1016/0022-247X(69)90031-6
[5] Karpagam, S.; Agrawal, Sushama: Best proximity point theorems for p-cyclic Meir--Keeler contractions, Fixed point theory appl. 2009 (2009) · Zbl 1172.54028 · doi:10.1155/2009/197308
[6] Al-Thagafi, M. A.; Shahzad, N.: Convergence and existence results for best proximity points, Nonlinear anal. 70, 3665-3671 (2009) · Zbl 1197.47067 · doi:10.1016/j.na.2008.07.022
[7] Eldred, A. A.; Kirk, W. A.; Veeramani, P.: Proximal normal structure and relatively non expansive mappings, Studia math. 171, No. 3, 283-293 (2005) · Zbl 1078.47013 · doi:10.4064/sm171-3-5
[8] Espinola, R.: A new approach to relatively nonexpansive mappings, Proc. amer. Math. soc. 136, No. 6, 1987-1995 (2008) · Zbl 1141.47035 · doi:10.1090/S0002-9939-08-09323-4
[9] T. Suzuki, M. Kikkawa, C. Vetro, The existence of best proximity points in metric spaces with the property UC, Nonlinear Anal. Available online. · Zbl 1178.54029 · doi:10.1016/j.na.2009.01.173