Publications (9)9.83 Total impact
 [Show abstract] [Hide abstract] ABSTRACT: We consider viscosity approximation methods with demicontinuous strong pseudocontractions for a nonexpansive semigroup. Strong convergence theorems of the purposed iterative process are established in the framework of Hilbert spaces.
 [Show abstract] [Hide abstract] ABSTRACT: In this paper, we introduce a modified Mann iterative process for strictly pseudocontractive mappings and obtain a strong convergence theorem in the framework of Hilbert spaces. Our results improve and extend the recent onesannounced by many others.
 [Show abstract] [Hide abstract] ABSTRACT: We consider a new algorithm for a generalized system for relaxed cocoercive nonlinear inequalities involving three different operators in Hilbert spaces by the convergence of projection methods. Our results include the previous results as special cases extend and improve the main results of R. U. Verma [J. Optimization Theory Appl. 121, No. 1, 203–210 (2004; Zbl 1056.49017)], S. S. Chang et al. [Appl. Math. Lett. 20, No. 3, 329–334 (2007; Zbl 1114.49008), Z. Y. Huang and M. A. Noor [Appl. Math. Comput. 190, No. 1, 356–361 (2007; Zbl 1120.65080)], and many others.

Article: Generalized Variational Inequalities Involving Relaxed Monotone Mappings and Nonexpansive Mappings
[Show abstract] [Hide abstract] ABSTRACT: We consider the solvability of generalized variational inequalities involving multivalued relaxed monotone operators and singlevalued nonexpansive mappings in the framework of Hilbert spaces. We also study the convergence criteria of iterative methods under some mild conditions. Our results improve and extend the recent ones announced by many others.  [Show abstract] [Hide abstract] ABSTRACT: Let E be a uniformly convex Banach space, and let K be a nonempty convex closed subset which is also a nonexpansive retract of E . Let T : K ® E be an asymptotically nonexpansive mapping with { k<sub>n</sub> } Ì [1, ¥ ) such that ( å from n =1 to ¥ )( k<sub>n</sub>  1) < ¥ and let F ( T ) be nonempty, where F ( T ) denotes the fixed points set of T . Let {a <sub>n</sub> } , {b <sub>n</sub> } , {g <sub>n</sub> } , {a¢ <sub>n</sub> } , {b¢ <sub>n</sub> } , {g¢ <sub>n</sub> } , {a¢¢ <sub>n</sub> } , {b¢¢ <sub>n</sub> } and {g¢¢ <sub>n</sub> } be real sequences in [0, 1] such that a <sub>n</sub> + b <sub>n</sub> + g <sub>n</sub> = a¢ <sub>n</sub> + b¢ <sub>n</sub> + g¢ <sub>n</sub> = a¢¢ <sub>n</sub> + b¢¢ <sub>n</sub> + g¢¢ <sub>n</sub> = 1 and e £ a <sub>n</sub> , a¢ <sub>n</sub> , a¢¢ <sub>n</sub> £ 1  e for all n Î N and some e > 0 , starting with arbitrary x <sub>1</sub> Î K ,define the sequence { x<sub>n</sub> } by setting z<sub>n</sub> = P ( a¢¢ <sub>n</sub> T ( PT )<sup> n 1</sup> x<sub>n</sub> + b¢¢ <sub>n</sub> x<sub>n</sub> + g¢¢ <sub>n</sub> w<sub>n</sub> ), y<sub>n</sub> =P ( a¢ <sub>n</sub> T ( PT )<sup> n 1</sup> z<sub>n</sub> + b¢ <sub>n</sub> x<sub>n</sub> + g¢ <sub>n</sub> v<sub>n</sub> ), x <sub> n +1</sub> = P ( a <sub>n</sub> T ( PT )<sup> n 1</sup> y<sub>n</sub> + b <sub>n</sub> x<sub>n</sub> + g <sub>n</sub> u<sub>n</sub> ), with the restrictions ( å from n =1 to ¥ ) ( g <sub>n</sub> ) < ¥ ,( å from n =1 to ¥ ) ( g¢ <sub>n</sub> ) < ¥ and ( å from n =1 to ¥ ) ( g¢¢ <sub>n</sub> ) < ¥ where { w<sub>n</sub> } , { v<sub>n</sub> } and { u<sub>n</sub> } are bounded sequences in K . (i) If E is realuniformly convex Banach space satisfying Opial's condition, then weak convergence of { x<sub>n</sub> } to some p Î F ( T ) is obtained; (ii) If T satisfies condition (A), then { x<sub>n</sub> } convergence strongly to some p Î F ( T ).
 [Show abstract] [Hide abstract] ABSTRACT: The purpose of this article is to prove strong convergence theorems for fixed points of closed hemirelatively nonexpansive mappings. In order to get these convergence theorems, the monotone hybrid iteration method is presented and is used to approximate those fixed points. Note that the hybrid iteration method presented by S. Matsushita and W. Takahashi can be used for relatively nonexpansive mapping, but it cannot be used for hemirelatively nonexpansive mapping. The results of this paper modify and improve the results of S. Matsushita and W. Takahashi (2005), and some others.

Article: Generalized Nonlinear Variational Inclusions Involving (A,ÃŽÂ·)Monotone Mappings in Hilbert Spaces
[Show abstract] [Hide abstract] ABSTRACT: A new class of generalized nonlinear variational inclusions involving (A,ÃŽÂ·)monotone mappings in the framework of Hilbert spaces is introduced and then based on the generalized resolvent operator technique associated with (A,ÃŽÂ·)monotonicity, the approximation solvability of solutions using an iterative algorithm is investigated. Since (A,ÃŽÂ·)monotonicity generalizes Amonotonicity and Hmonotonicity, results obtained in this paper improve and extend many others.  [Show abstract] [Hide abstract] ABSTRACT: We show that the general variational inequalities are equivalent to the general WienerHopf equations and use this alterative equivalence to suggest and analyze a new iterative method for finding the common element of the set of fixed points of a nonexpansive mapping and the set of solutions of the general variational inequality involving multivalued relaxed monotone operators. Our results improve and extend recent ones announced by many others. Copyright (c) 2007 Yongfu Su et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
 [Show abstract] [Hide abstract] ABSTRACT: We modified the classic Mann iterative process to have strong convergence theorem for a finite family of nonexpansive mappings in the framework of Hilbert spaces. Our results improve and extend the results announced by many others.
Publication Stats
120  Citations  
9.83  Total Impact Points  
Top Journals
Institutions

20092010

Shijiazhuang Tiedao University
Chentow, Hebei, China


20072008

Tianjin Polytechnic University
T’ienchingshih, Tianjin Shi, China 
Gyeongsang National University
 Department of Mathematics
Shinshū, Gyeongsangnamdo, South Korea
