CFP last date
22 July 2024
Call for Paper
August Edition
IJCA solicits high quality original research papers for the upcoming August edition of the journal. The last date of research paper submission is 22 July 2024

Submit your paper
Know more
The week's pick
Responsive image
Implementation of Polynomial Regression using Least Squares and Gradient Descent in Python

Ahmad Farhan AlShammari
Random Articles
Reseach Article

A New Iterative Scheme for Nonexpansive and Monotone Lipschitz Continuous Mappings

by Renu Chugh, Rekha Rani
journal cover thumbnail

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

Powered by PhDFocusTM