An implicit method for finding common solutions of variational inequalities and systems of equilibrium problems and fixed points of infinite family of nonexpansive mappings

作者: Vittorio Colao , Genaro López Acedo , Giuseppe Marino

DOI: 10.1016/J.NA.2009.01.115

关键词:

摘要: Abstract Let H be a Hilbert space. Consider on sequence of nonexpansive mappings { T n } with common fixed points, finite family equilibrium functions G i = 1 , … K contraction f coefficient 0 α and strongly positive linear bounded operator A γ ¯ > . / Assuming there are points the which also for we define suitable converges to unique such point satisfies variational inequality 〈 ( − ) x ∗ 〉 ≥ all in intersection

参考文章(30)
W Oettli, E. Blum, From optimization and variational inequalities to equilibrium problems Math. Student. ,vol. 63, pp. 123- 145 ,(1994)
H.K. Xu, An Iterative Approach to Quadratic Optimization Journal of Optimization Theory and Applications. ,vol. 116, pp. 659- 678 ,(2003) , 10.1023/A:1023073621589
W. A. Kirk, Kazimierz Goebel, Topics in metric fixed point theory ,(1990)
Louis Nirenberg, Haim Brezis, G. Stampacchia, A remark on Ky fan's minimax principle Bollettino Della Unione Matematica Italiana. ,vol. 1, pp. 257- 264 ,(2008)
Wataru Takahashi, Kazuya Shimoji, STRONG CONVERGENCE TO COMMON FIXED POINTS OF INFINITE NONEXPANSIVE MAPPINGS AND APPLICATIONS Taiwanese Journal of Mathematics. ,vol. 5, pp. 387- 404 ,(2001) , 10.11650/TJM.5.2001.1233
George Allen, Variational inequalities, complementarity problems, and duality theorems Journal of Mathematical Analysis and Applications. ,vol. 58, pp. 1- 10 ,(1977) , 10.1016/0022-247X(77)90222-0
K.A. Stewart, Image Recovery—Theory and Applications Electronics and Power. ,vol. 33, pp. 747- ,(1987) , 10.1049/EP.1987.0438
Somyot Plubtieng, Rattanaporn Punpaeng, A general iterative method for equilibrium problems and fixed point problems in Hilbert spaces Journal of Mathematical Analysis and Applications. ,vol. 336, pp. 455- 469 ,(2007) , 10.1016/J.JMAA.2007.02.044