## Publications (9)9.83 Total impact

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**ABSTRACT:**We consider viscosity approximation methods with demi-continuous strong pseudo-contractions for a non-expansive semigroup. Strong convergence theorems of the purposed iterative process are established in the framework of Hilbert spaces.Journal of Inequalities and Applications 01/2010; 2010(1). DOI:10.1155/2010/645498 · 0.77 Impact Factor - [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.Modern Applied Science 01/2009; DOI:10.5539/mas.v1n3p19 - [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.Modern Applied Science 01/2009; DOI:10.1155/2007/45398 -
##### Article: Generalized Variational Inequalities Involving Relaxed Monotone Mappings and Nonexpansive Mappings

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**ABSTRACT:**We consider the solvability of generalized variational inequalities involving multivalued relaxed monotone operators and single-valued 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.Journal of Inequalities and Applications 01/2008; 2007(1). DOI:10.1155/2007/20457 · 0.77 Impact Factor - [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 ).01/2008; - [Show abstract] [Hide abstract]

**ABSTRACT:**The purpose of this article is to prove strong convergence theorems for fixed points of closed hemi-relatively 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 hemi-relatively nonexpansive mapping. The results of this paper modify and improve the results of S. Matsushita and W. Takahashi (2005), and some others.Fixed Point Theory and Applications 01/2008; 2008(2). DOI:10.1155/2008/284613 · 2.50 Impact Factor -
##### Article: Generalized Nonlinear Variational Inclusions Involving (A,ÃŽÂ·)-Monotone Mappings in Hilbert Spaces

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**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 A-monotonicity and H-monotonicity, results obtained in this paper improve and extend many others.Fixed Point Theory and Applications 01/2008; 2007(1). DOI:10.1155/2007/29653 · 2.50 Impact Factor - [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.Fixed Point Theory and Applications 01/2007; DOI:10.1155/2007/76971 · 2.50 Impact Factor - [Show abstract] [Hide abstract]

**ABSTRACT:**We show that the general variational inequalities are equivalent to the general Wiener-Hopf 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.Journal of Inequalities and Applications 01/2007; DOI:10.1155/2007/64947 · 0.77 Impact Factor

#### Publication Stats

94 | Citations | |

9.83 | Total Impact Points | |