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)
One-step iterative process for a finite family of multivalued mappings. (English) Zbl 1225.65059
Summary: We introduce a one-step iterative process to approximate common fixed points of a finite family of generalized nonexpansive multivalued mappings and prove some weak and strong convergence theorems for such mappings in uniformly convex Banach spaces.
MSC:
65J15Equations with nonlinear operators (numerical methods)
47H10Fixed point theorems for nonlinear operators on topological linear spaces
47J25Iterative procedures (nonlinear operator equations)
References:
[1]Markin, J.: A fixed point theorem for set valued mappings, Bull. amer. Math. soc. 74, 639-640 (1968) · Zbl 0159.19903 · doi:10.1090/S0002-9904-1968-11971-8
[2]Jr., S. B. Nadler: Multi-valued contraction mappings, Pacific J. Math. 30, 475-488 (1969) · Zbl 0187.45002
[3]Sastry, K. P. R.; Babu, G. V. R.: Convergence of Ishikawa iterates for a multivalued mapping with a fixed point, Czechoslovak math. J. 55, 817-826 (2005) · Zbl 1081.47069 · doi:10.1007/s10587-005-0068-z
[4]Panyanak, B.: Mann and Ishikawa iterative processes for multivalued mappings in Banach spaces, Comput. math. Appl. 54, 872-877 (2007) · Zbl 1130.47050 · doi:10.1016/j.camwa.2007.03.012
[5]Song, Y.; Wang, H.: Erratum to Mann and Ishikawa iterative processes for multivalued mappings in Banach spaces, Comput. math. Appl. 55, 2999-3002 (2008) · Zbl 1142.47344 · doi:10.1016/j.camwa.2007.11.042
[6]Song, Y.; Wang, H.: Convergence of iterative algorithms for multivalued mappings in Banach spaces, Nonlinear anal. 70, 1547-1556 (2009) · Zbl 1175.47063 · doi:10.1016/j.na.2008.02.034
[7]Shahzad, N.; Zegeye, H.: On Mann and Ishikawa iteration schemes for multivalued maps in Banach space, Nonlinear anal. 71, 838-844 (2009) · Zbl 1218.47118 · doi:10.1016/j.na.2008.10.112
[8]Abbas, M.; Khan, S. H.; Khan, A. R.; Agarwal, R. P.: Common fixed points of two multivalued nonexpansive mappings by one-step iterative scheme, Appl. math. Lett. 24, 97-102 (2011) · Zbl 1223.47068 · doi:10.1016/j.aml.2010.08.025
[9]Suzuki, T.: Fixed point thoerems and convergence theorems for some generelized nonexpansive mappings, J. math. Anal. appl. 340, 1088-1095 (2008) · Zbl 1140.47041 · doi:10.1016/j.jmaa.2007.09.023
[10]Abkar, A.; Eslamian, M.: Fixed point theorems for Suzuki generalized nonexpansive multivalued mappings in Banach spaces, Fixed point theory appl. 2010 (2010) · Zbl 1205.47051 · doi:10.1155/2010/457935
[11]Xu, H. K.: Inequalities in Banach spaces with application, Nonlinear anal. 16, 1127-1138 (1991)
[12]Cho, Y. J.; Zhou, H. Y.; Guo, G.: Weak and strong convergence theorems for three-step iterations with errors for asymptotically nonexpansive mappings, Comput. math. Appl. 47, 707-717 (2004) · Zbl 1081.47063 · doi:10.1016/S0898-1221(04)90058-2
[13]Nammanee, K.; Noor, M. A.; Suantai, S.: Convergence criteria of modified Noor iterations with errors for asymptotically nonexpansive mappings, J. math. Anal. appl. 314, 320-334 (2006) · Zbl 1087.47054 · doi:10.1016/j.jmaa.2005.03.094