A hybrid algorithm with Meir-Keeler contraction for asymptotically pseudocontractive mappings

Volume 9, Issue 6, pp 4772--4779 http://dx.doi.org/10.22436/jnsa.009.06.114

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 1468 Downloads
• 2588 Views

Authors

Youli Yu - School of Mathematics and Information Engineering, Taizhou University, Linhai 317000, China. Ching-Feng Wen - Center for Fundamental Science, and Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung, Kaohsiung, 807, Taiwan. Xiaoyin Wang - Department of Mathematics, Tianjin Polytechnic University, Tianjin 300387, China.

Abstract

A hybrid algorithm with Meir-Keeler contraction for finding the fixed points of the asymptotically pseudocontractive mappings is presented. Some strong convergence results are given.

Share and Cite

Keywords

• Asymptotically pseudocontractive mapping
• hybrid algorithm
• fixed point.

MSC

•  47J25
•  47H09

References

• [1] L. C. Ceng, A. Petrusel, J. C. Yao, Strong convergence of modified implicit iterative algorithms with perturbed mappings for continuous pseudocontractive mappings, Appl. Math. Comput., 209 (2009), 162--176


• [2] C. E. Chidume, Strong convergence theorems for fixed points of asymptotically pseudocontractive semi-groups, J. Math. Anal. Appl., 296 (2004), 410--421


• [3] C. E. Chidume, M. Abbas, B. Ali, Convergence of the Mann iteration algorithm for a class of pseudocontractive mappings, Appl. Math. Comput., 194 (2007), 1--6


• [4] R. Dewangan, B. S. Thakur, M. Postolache, Strong convergence of asymptotically pseudocontractive semigroup by viscosity iteration, Appl. Math. Comput., 248 (2014), 160--168


• [5] F. Gu, Approximate fixed point sequence for a finite family of asymptotically pseudocontractive mappings, Comput. Math. Appl., 53 (2007), 1792--1799


• [6] J. K. Kim, Y. M. Nam, Modified Ishikawa iterative sequences with errors for asymptotically set-valued pseudo- contractive mappings in Banach spaces, Bull. Korean Math. Soc., 43 (2006), 847--860


• [7] A. Meir, E. Keeler, A theorem on contraction mappings, J. Math. Anal. Appl., 28 (1969), 326--329


• [8] C. Moore, B. V. C. Nnoli, Strong convergence of averaged approximants for Lipschitz pseudocontractive maps, J. Math. Anal. Appl., 260 (2001), 269--278


• [9] U. Mosco, Convergence of convex sets and of solutions of variational inequalities, Advances in Math., 3 (1969), 510--585


• [10] E. U. Ofoedu, Strong convergence theorem for uniformly L-Lipschitzian asymptotically pseudocontractive mapping in real Banach space, J. Math. Anal. Appl., 321 (2006), 722--728


• [11] J. Schu, Iterative construction of fixed points of asymptotically nonexpansive mappings, J. Math. Anal. Appl., 158 (1991), 407--413


• [12] T. Suzuki, Moudafi's viscosity approximations with Meir-Keeler contractions, J. Math. Anal. Appl., 325 (2007), 342--352


• [13] M. Tsukada, Convergence of best approximations in a smooth Banach space, J. Approx. Theory, 40 (1984), 301--309


• [14] A. Udomene, Path convergence, approximation of fixed points and variational solutions of Lipschitz pseudocontractions in Banach spaces, Nonlinear Anal., 67 (2007), 2403--2414


• [15] Y. Yao, R. P. Agarwal, M. Postolache, Y. C. Liou, Algorithms with strong convergence for the split common solution of the feasibility problem and fixed point problem, Fixed Point Theory and Appl., 2014 (2014), 14 pages


• [16] Y. Yao, W. Jigang, Y. C. Liou, Regularized methods for the split feasibility problem, Abstr. Appl. Anal., 2012 (2012), 15 pages


• [17] Y. Yao, Y. C. Liou, J. C. Yao, Split common fixed point problem for two quasi-pseudo-contractive operators and its algorithm construction, Fixed Point Theory and Appl., 2015 (2015), 19 pages


• [18] Y. Yao, G. Marino, H. K. Xu, Y. C. Liou, Construction of minimum-norm fixed points of pseudocontractions in Hilbert spaces, J. Inequal. Appl., 2014 (2014), 14 pages


• [19] Y. Yao, M. Postolache, S. M. Kang, Strong convergence of approximated iterations for asymptotically pseudocontractive mappings, Fixed Point Theory and Appl., 2014 (2014), 13 pages


• [20] Y. Yao, M. Postolache, Y. C. Liou, Coupling Ishikawa algorithms with hybrid techniques for pseudocontractive mappings, Fixed Point Theory and Appl., 2013 (2013), 8 pages


• [21] Y. Yao, M. Postolache, Y. C. Liou, Strong convergence of a self-adaptive method for the split feasibility problem, Fixed Point Theory and Appl., 2013 (2013), 12 pages


• [22] H. Zegeye, M. Robdera, B. Choudhary, Convergence theorems for asymptotically pseudocontractive mappings in the intermediate sense, Comput. Math. Appl., 62 (2011), 326--332


• [23] H. Zegeye, N. Shahzad, An algorithm for a common fixed point of a family of pseudocontractive mappings, Fixed Point Theory and Appl., 2013 (2013), 14 pages


• [24] H. Zegeye, N. Shahzad, T. Mekonen, Viscosity approximation methods for pseudocontractive mappings in Banach spaces, Appl. Math. Comput., 185 (2007), 538--546


• [25] H. Zhou, Demiclosedness principle with applications for asymptotically pseudo-contractions in Hilbert spaces, Nonlinear Anal., 70 (2009), 3140--3145