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A New Iterative Scheme for Nonexpansive and Monotone Lipschitz Continuous Mappings

by Renu Chugh, Rekha Rani
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International Journal of Computer Applications
Foundation of Computer Science (FCS), NY, USA
Volume 91 - Number 8
Year of Publication: 2014
Authors: Renu Chugh, Rekha Rani
10.5120/15905-5180

Renu Chugh, Rekha Rani . A New Iterative Scheme for Nonexpansive and Monotone Lipschitz Continuous Mappings. International Journal of Computer Applications. 91, 8 ( April 2014), 42-45. DOI=10.5120/15905-5180

@article{ 10.5120/15905-5180,
author = { Renu Chugh, Rekha Rani },
title = { A New Iterative Scheme for Nonexpansive and Monotone Lipschitz Continuous Mappings },
journal = { International Journal of Computer Applications },
issue_date = { April 2014 },
volume = { 91 },
number = { 8 },
month = { April },
year = { 2014 },
issn = { 0975-8887 },
pages = { 42-45 },
numpages = {9},
url = { https://ijcaonline.org/archives/volume91/number8/15905-5180/ },
doi = { 10.5120/15905-5180 },
publisher = {Foundation of Computer Science (FCS), NY, USA},
address = {New York, USA}
}
%0 Journal Article
%1 2024-02-06T22:12:16.278730+05:30
%A Renu Chugh
%A Rekha Rani
%T A New Iterative Scheme for Nonexpansive and Monotone Lipschitz Continuous Mappings
%J International Journal of Computer Applications
%@ 0975-8887
%V 91
%N 8
%P 42-45
%D 2014
%I Foundation of Computer Science (FCS), NY, USA
Abstract

The aim of paper is to prove a weak convergenceresult for finding a common of the set of fixed points of a nonexpansive mapping and the set of solutions of a variational inequality problem for a monotone, Lipschitz continuous mapping. Using an example in C++, validity of the result will be proved. Also, we shall find a common element of the set of fixed points of a nonexpansive mapping and the set of zeros of a monotone, Lipschitz continuous mapping.

References
  1. Browder F E and Petryshyn W V (1967) Construction of Fixed Points of non-linear Mapping in Hilbert Spaces J Math Anal Appl 20 197-228.
  2. Browder F E (1965) Fixed-point Theorems for Noncompact Mappings in Hilbert Space Proc Natl Acad Sci U S A 53 1272-1276.
  3. Goebel K and Kirk W A (1990) Topics in Metric Fixed Point Theory vol. 28 of Cambridge Studies in Advanced Mathematics, Cambridge University Press, Cambridge, UK.
  4. Iiduka H and Takahashi W (2004), Stronge convergence theorems for nonexpansive nonself mappings and inverse strongly monotone mappings, J convex Anal, vol 11, 69-79.
  5. Liu F and Nashed M Z (1998) Regularization of Non-linear Ill- posed Variational inequalities and convergence rates,Set-valued Anal 6 313-344.
  6. Matsushita S and Kuroiwa, Approximation of fixed points of nonexpansive nonself mappings, Sci Math Jpn, vol 57(2003), 171-176.
  7. Opial Z (1967) Weak convergence of the sequence of successive Approximations of Nonexpansive Mappings Bull Am Math Soc 73 591-597.
  8. Rockafellar R T (1970) On the Maximality of Sums of nonlinear Monotone Operators Trans Amer Math Soc 149 75-88.
  9. Schu J (1991) Weak and Strong Convergence to fixed points of Asymptotically nonexpansive Mappings Bull Aust Math Soc 43, 153-159.
  10. Takahashi W (2000) Non-linear functional Analysis Yokohama Publisher, Yokohama Japan.
  11. Takahashi W, Tamura T (1998) Convergence Theorems for a pair of nonexpansive Mapping J Convex Anal 5 45-56.
  12. Takahashi W and Toyoda M (2003) Weak Convergence Theorems for Non-expansive Mappings and Monotone Mappings J Optim Theory Appl 118 417-428.
  13. Yamda I (2001) The Hybrid Steepest-Descent Method for the Variational Inequality Problem over the Intersection of fixed-point Sets of nonexpansive Mapping, inherently Parallel Algorithms in Feasibility and Optimization and their applications, Edited by D. Butnariu, y. Censor, and S. Reich, kluwer Academic Pulishers, Dordrecht, Holland, 473-504.
Index Terms

Computer Science
Information Sciences

Keywords

Fixed Points Hilbert Spaces Monotone Mappings Nonexpansive Mappings Variational Inequalities. 2000 Mathematics Subject Classification: Primary 47H05 47J05 47J25

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