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)
A modified Halpern’s iterative scheme for solving split feasibility problems. (English) Zbl 1253.65093
Summary: We introduce and study a modified Halpern’s iterative scheme for solving the split feasibility problem (SFP) in the setting of infinite-dimensional Hilbert spaces. Under suitable conditions a strong convergence theorem is established. The main result presented in this paper improves and extends some recent results done by {\it H.-K. Xu} [Inverse Probl. 26, No. 10, Article ID 105018, 17 p. (2010; Zbl 1213.65085)] and some others.

MSC:
65J22Inverse problems (numerical methods in abstract spaces)
49N45Inverse problems in calculus of variations
47J25Iterative procedures (nonlinear operator equations)
47J06Nonlinear ill-posed problems
WorldCat.org
Full Text: DOI
References:
[1] Y. Censor and T. Elfving, “A multiprojection algorithm using Bregman projections in a product space,” Numerical Algorithms, vol. 8, no. 2-4, pp. 221-239, 1994. · Zbl 0828.65065 · doi:10.1007/BF02142692
[2] C. Byrne, “Iterative oblique projection onto convex sets and the split feasibility problem,” Inverse Problems, vol. 18, no. 2, pp. 441-453, 2002. · Zbl 0996.65048 · doi:10.1088/0266-5611/18/2/310
[3] Q. Yang, “The relaxed CQ algorithm solving the split feasibility problem,” Inverse Problems, vol. 20, no. 4, pp. 1261-1266, 2004. · Zbl 1066.65047 · doi:10.1088/0266-5611/20/4/014
[4] H.-K. Xu, “Iterative methods for the split feasibility problem in infinite-dimensional Hilbert spaces,” Inverse Problems, vol. 26, no. 10, Article ID 105018, 2010. · Zbl 1213.65085 · doi:10.1088/0266-5611/26/10/105018
[5] H.-K. Xu, “Averaged mappings and the gradient-projection algorithm,” Journal of Optimization Theory and Applications, vol. 150, no. 2, pp. 360-378, 2011. · Zbl 1233.90280 · doi:10.1007/s10957-011-9837-z
[6] F. E. Browder, “Fixed-point theorems for noncompact mappings in Hilbert space,” Proceedings of the National Academy of Sciences of the United States of America, vol. 53, no. 6, pp. 1272-1276, 1965. · Zbl 0125.35801 · doi:10.1073/pnas.53.6.1272
[7] M. O. Osilike and D. I. Igbokwe, “Weak and strong convergence theorems for fixed points of pseudocontractions and solutions of monotone type operator equations,” Computers & Mathematics with Applications, vol. 40, no. 4-5, pp. 559-567, 2000. · Zbl 0958.47030 · doi:10.1016/S0898-1221(00)00179-6
[8] H.-K. Xu, “Viscosity approximation methods for nonexpansive mappings,” Journal of Mathematical Analysis and Applications, vol. 298, no. 1, pp. 279-291, 2004. · Zbl 1061.47060 · doi:10.1016/j.jmaa.2004.04.059