publication . Article . 2011

Some results on a general iterative method for k-strictly pseudo-contractive mappings

Jung Jong Soo;
Open Access English
  • Published: 01 Jan 2011 Journal: Fixed Point Theory and Applications (issn: 1687-1820, eissn: 1687-1812, Copyright policy)
  • Publisher: SpringerOpen
Abstract
<p>Abstract</p> <p>Let <it>H </it>be a Hilbert space, <it>C </it>be a closed convex subset of <it>H </it>such that <it>C </it>&#177; <it>C </it>&#8834; <it>C</it>, and <it>T </it>: <it>C </it>&#8594; <it>H </it>be a <it>k</it>-strictly pseudo-contractive mapping with <it>F</it>(<it>T</it>) &#8800; &#8709; for some 0 &#8804; <it>k &lt; </it>1. Let <it>F </it>: <it>C </it>&#8594; <it>C </it>be a <it>&#954;</it>-Lipschitzian and <it>&#951;</it>-strongly monotone operator with <it>&#954; &gt; </it>0 and <it>&#951; &gt; </it>0 and <it>f </it>: <it>C </it>&#8594; <it>C </it>be a contraction with the contractive constant <it>&#945; </it>&#8712; (0, 1). Let <inline-form...
Subjects
free text keywords: Iterative schemes, <it>k</it>-strictly pseudo-contractive mapping, Nonexpansive mapping, Fixed points, Contraction, <it>&#954;</it>-Lipschitzian, <it>&#951;</it>-strongly monotone operator, Variational inequality, Hilbert space, Applied mathematics. Quantitative methods, T57-57.97, Analysis, QA299.6-433
Download from
19 references, page 1 of 2

1. Browder, FE: Fixed point theorems for noncompact mappings. Proc Natl Acad Sci USA. 53, 1272-1276 (1965). doi:10.1073/pnas.53.6.1272 [OpenAIRE]

2. Browder, FE: Convergence of approximants to fixed points of nonexpansive nonlinear mappings in Banach spaces. Arch Ration Mech Anal. 24, 82-90 (1967) [OpenAIRE]

3. Browder, FE, Petryshn, WV: Construction of fixed points of nonlinear mappings Hilbert space. J Math Anal Appl. 20, 197-228 (1967). doi:10.1016/0022-247X(67)90085-6 [OpenAIRE]

4. Acedo, GL, Xu, HK: Iterative methods for strictly pseudo-contractions in Hilbert space. Nonlinear Anal. 67, 2258-2271 (2007). doi:10.1016/j.na.2006.08.036

5. Cho, YJ, Kang, SM, Qin, X: Some results on k-strictly pseudo-contractive mappings in Hilbert spaces. Nonlinear Anal. 70, 1956-1964 (2009). doi:10.1016/j.na.2008.02.094

6. Jung, JS: Strong convergence of iterative methods for k-strictly pseudo-contractive mappings in Hilbert spaces. Appl Math Comput. 215, 3746-3753 (2010). doi:10.1016/j.amc.2009.11.015

7. Morales, CH, Jung, JS: Convergence of paths for pseudo-contractive mappings in Banach spaces. Proc Am Math Soc. 128, 3411-3419 (2000). doi:10.1090/S0002-9939-00-05573-8

8. Moudafi, A: Viscosity approximation methods for fixed-points problems. J Math Anal Appl. 241, 46-55 (2000). doi:10.1006/jmaa.1999.6615 [OpenAIRE]

9. Xu, HK: Viscosity approximation methods for nonexpansive mappings. J Math Anal Appl. 298, 279-291 (2004). doi:10.1016/j.jmaa.2004.04.059

10. Marino, G, Xu, HX: A general iterative method for nonexpansive mappings in Hilbert spaces. J Math Anal Appl. 318, 43-52 (2006). doi:10.1016/j.jmaa.2005.05.028

11. Yamada, I: The hybrid steepest descent for the variational inequality problems over the intersection of fixed points sets of nonexpansive mappings. In: Butnariu D, Censor Y, Reich S (eds.) Inherently Parallel Algorithms in Feasibility and Optimization and Their Applications. pp. 473-504. Elservier, New York (2001)

12. Tian, M: A general itewrative algorithm for nonexpansive mappings in Hilbert spaces. Nonlinear Anal. 73, 689-694 (2010). doi:10.1016/j.na.2010.03.058

13. Halpern, B: Fixed points of nonexpansive maps. Bull Am Math Soc. 73, 957-961 (1967). doi:10.1090/S0002-9904-1967- 11864-0 [OpenAIRE]

14. Wittmann, R: Approximation of fixed points of nonexpansive mappings. Arch Math. 58, 486-491 (1992). doi:10.1007/ BF01190119 [OpenAIRE]

15. Zhou, H: Convergence theorems of fixed points for k-strict pseudo-contractions in Hilbert spaces. Nonlinear Anal. 69, 456-462 (2008). doi:10.1016/j.na.2007.05.032

19 references, page 1 of 2
Powered by OpenAIRE Research Graph
Any information missing or wrong?Report an Issue