zbMATH — the first resource for mathematics

Examples
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.

Operators
a & b logic and
a | b logic or
!ab logic not
abc* right wildcard
"ab c" phrase
(ab c) parentheses
Fields
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)
On fixed point generalizations of Suzuki’s method. (English) Zbl 05883254
Summary: In order to generalize the well-known Banach contraction theorem, many authors have introduced various types of contraction inequalities. In 2008, Suzuki introduced a new method (Suzuki (2008) [4]) and then his method was extended by some authors (see for example, Dhompongsa and Yingtaweesittikul (2009), Kikkawa and Suzuki (2008) and Mot and Petrusel (2009) [7], [10], [5] and [6]). Kikkawa and Suzuki extended the method in (Kikkawa and Suzuki (2008) [5]) and then Mot and Petrusel further generalized it in (Mot and Petrusel (2009) [6]). In this paper, we shall provide a new condition for T which guarantees the existence of its fixed point. Our results generalize some old results.
MSC:
46Functional analysis
References:
[1]Petrusel, A.: Operatorial inclusions, (2002)
[2]Kannan, R.: Some results on fixed points II, American mathematical monthly 76, 405-408 (1969) · Zbl 0179.28203 · doi:10.2307/2316437
[3]Subrahmanyam, P. V.: Completeness and fixed points, Monatshefte für Mathematik 74, No. 4, 325-330 (1969)
[4]Suzuki, T.: A generalized Banach contraction principle that characterized metric completeness, Proceedings of the American mathematical society 136, 1861-1869 (2008) · Zbl 1145.54026 · doi:10.1090/S0002-9939-07-09055-7
[5]Kikkawa, M.; Suzuki, T.: Three fixed point theorems for generalized contractions with constants in complete metric spaces, Nonlinear analysis 69, 2942-2949 (2008) · Zbl 1152.54358 · doi:10.1016/j.na.2007.08.064
[6]Mot, G.; Petrusel, A.: Fixed point theory for a new type of contractive multivalued operators, Nonlinear analysis 70, 3371-3377 (2009) · Zbl 1213.54068 · doi:10.1016/j.na.2008.05.005
[7]S. Dhompongsa, H. Yingtaweesittikul, Fixed point for multivalued mappings and the metric completeness, Fixed Point Theory and Applications, 2009, 15 pages, Article ID 972395. doi:10.1155/2009/972395. · Zbl 1179.54055 · doi:10.1155/2009/972395
[8]Reich, S.: Kannan’s fixed point theorem, Bollettino Della unione matematica italiana. Serie 9 4, 1-11 (1971) · Zbl 0219.54042
[9]Constantin, A.: A random fixed point theorem for multifunctions, Stochastic analysis and applications 12, No. 1, 65-73 (1994) · Zbl 0813.60058 · doi:10.1080/07362999408809338
[10]M. Kikkawa, T. Suzuki, Some similarity between contractions and Kannan mappings, Fixed Point Theory and Applications, 2008, 8 pages, Article ID 649749. doi:10.1155/2008/649749. · Zbl 1162.54019 · doi:10.1155/2008/649749