Abstract
In this paper, strong convergence theorem is obtained for the modified Noor iterations in the framework of uniformly smooth Banach spaces. Our results extend and improve the recent ones announced by Wittman, Kim, Xu, and some others.
In this paper, strong convergence theorem is obtained for the modified Noor iterations in the framework of uniformly smooth Banach spaces. Our results extend and improve the recent ones announced by Wittman, Kim, Xu, and some others.
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, pp. 1272–1276, 1965.
View at: Google Scholar | Zentralblatt MATH | MathSciNetF. E. Browder, “Convergence of approximants to fixed points of nonexpansive non-linear mappings in Banach spaces,” Archive for Rational Mechanics and Analysis, vol. 24, no. 1, pp. 82–90, 1967.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetR. E. Bruck, Jr., “Nonexpansive projections on subsets of Banach spaces,” Pacific Journal of Mathematics, vol. 47, pp. 341–355, 1973.
View at: Google Scholar | Zentralblatt MATH | MathSciNetK. Goebel and S. Reich, Uniform Convexity, Hyperbolic Geometry, and Nonexpansive Mappings, vol. 83 of Monographs and Textbooks in Pure and Applied Mathematics, Marcel Dekker, New York, 1984.
View at: Google Scholar | Zentralblatt MATH | MathSciNetB. Halpern, “Fixed points of nonexpanding maps,” Bulletin of the American Mathematical Society. New Series, vol. 73, pp. 957–961, 1967.
View at: Google Scholar | Zentralblatt MATH | MathSciNetT. H. Kim and H. K. Xu, “Strong convergence of modified Mann iterations,” Nonlinear Analysis, vol. 61, no. 1-2, pp. 51–60, 2005.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetP.-L. Lions, “Approximation de points fixes de contractions,” Comptes Rendus Mathematique. Academie des Sciences. Paris Série A-B, vol. 284, no. 21, pp. A1357–A1359, 1977.
View at: Google Scholar | Zentralblatt MATH | MathSciNetS. Reich, “Asymptotic behavior of contractions in Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 44, no. 1, pp. 57–70, 1973.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetS. Reich, “Strong convergence theorems for resolvents of accretive operators in Banach spaces,” Journal of Mathematical Analysis and Applications, vol. 75, no. 1, pp. 287–292, 1980.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetS. Reich, “Approximating fixed points of nonexpansive mappings,” Panamerican Mathematical Journal, vol. 4, no. 2, pp. 23–28, 1994.
View at: Google Scholar | Zentralblatt MATH | MathSciNetR. Wittmann, “Approximation of fixed points of nonexpansive mappings,” Archiv der Mathematik, vol. 58, no. 5, pp. 486–491, 1992.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetH. K. Xu, “Iterative algorithms for nonlinear operators,” Journal of the London Mathematical Society. Second Series, vol. 66, no. 1, pp. 240–256, 2002.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNetH. K. Xu, “An iterative approach to quadratic optimization,” Journal of Optimization Theory and Applications, vol. 116, no. 3, pp. 659–678, 2003.
View at: Publisher Site | Google Scholar | Zentralblatt MATH | MathSciNet