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 theorems in partially ordered complete metric spaces. (English) Zbl 1225.54030
Summary: We present some fixed point theorems in a partially ordered complete metric space $X$. The usual Caristi’s condition that $x\preceq Tx$ for each $x\in X$ is weakened at the expense that the mapping is nondecreasing with respect to a partial order.

54H25Fixed-point and coincidence theorems in topological spaces
65J15Equations with nonlinear operators (numerical methods)
47H10Fixed-point theorems for nonlinear operators on topological linear spaces
47J25Iterative procedures (nonlinear operator equations)
Full Text: DOI
[1] Feng, Y. Q.; Liu, S. Y.: Fixed point theorems for multi-valued contractive mappings and multi-valued caristi type mappings, J. math. Anal. appl. 317, 103-112 (2006) · Zbl 1094.47049 · doi:10.1016/j.jmaa.2005.12.004
[2] Khamsi, M. A.: Remarks on caristi’s fixed point theorem, Nonlinear anal. 71, 227-231 (2009) · Zbl 1175.54056 · doi:10.1016/j.na.2008.10.042
[3] Li, Z.: Remarks on caristi’s fixed point theorem and kirk’s problem, Nonlinear anal.tma 73, 3751-3755 (2010) · Zbl 1201.54036 · doi:10.1016/j.na.2010.07.048
[4] Kirk, W. A.; Caristi, J.: Mapping theorems in metric and Banach spaces, Bull. acad. Pol sci. 23, 891-894 (1975) · Zbl 0313.47041
[5] Kirk, W. A.: Caristi’s fixed-point theorem and metric convexity, Colloq. math. 36, 81-86 (1976) · Zbl 0353.53041
[6] Caristi, J.: Fixed point theorems for mappings satisfying inwardness conditions, Trans. amer. Math. soc. 215, 241-251 (1976) · Zbl 0305.47029 · doi:10.2307/1999724
[7] Browder, F. E.: On a theorem of caristi and kirk, , 23-27 (1975) · Zbl 0379.54016
[8] Downing, D.; Kirk, W. A.: A generalization of caristi’s theorem with applications to nonlinear mapping theory, Pacific J. Math. 69, 339-345 (1977) · Zbl 0357.47036
[9] Downing, D.; Kirk, W. A.: Fixed point theorems for set-valued mappings in metric and Banach spaces, Math. japon. 22, 99-112 (1977) · Zbl 0372.47030
[10] Khamsi, M. A.; Misane, D.: Compactness of convexity structures in metrics paces, Math. japon. 41, 321-326 (1995) · Zbl 0824.54026
[11] Jachymski, J. R.: Converses to fixed point theorems of zeremlo and caristi, Nonlinear anal. 52, 1455-1463 (2003) · Zbl 1030.54033 · doi:10.1016/S0362-546X(02)00177-3
[12] Jachymski, J. R.: Caristi’s fixed point theorem and selection of set-valued contractions, J. math. Anal. appl. 227, 55-67 (1998) · Zbl 0916.47044 · doi:10.1006/jmaa.1998.6074
[13] Bae, J. S.: Fixed point theorems for weakly contractive multivalued maps, J. math. Anal. appl. 284, 690-697 (2003) · Zbl 1033.47038 · doi:10.1016/S0022-247X(03)00387-1
[14] Suzuki, T.: Generalized caristi’s fixed point theorems by bae and others, J. math. Anal. appl. 302, 502-508 (2005) · Zbl 1059.54031 · doi:10.1016/j.jmaa.2004.08.019
[15] Amini-Harandi, A.: Some generalizations of caristi’s fixed point theorem with application to the fixed point theory of weakly contractive set-valued maps and the minimization problem, Nonlinear anal. TMA 72, 4661-4665 (2010) · Zbl 1222.47081 · doi:10.1016/j.na.2010.02.045