Publications (7)7.48 Total impact

Article: Strong convergence of modified Halpern’s iterations for a kstrictly pseudocontractive mapping
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ABSTRACT: In this paper, we discuss three modified Halpern iterations as follows: x n+1 =α n u+(1α n )((1δ)x n +δTx n ),(I) x n+1 =α n ((1δ)u+δx n )+(1α n )Tx n ,( II ) x n+1 =α n u+β n x n +y n Tx n ,n≥0,( III ) and obtained strong convergence results for the iterations (I)–(III) for a kstrictly pseudocontractive mapping, where {α n } satisfies the conditions: (C1) lim n→∞ α n =0 and (C2) ∑ n=1 ∞ α n =+∞, respectively. The results presented in this work improve the corresponding ones by many other authors.  [Show abstract] [Hide abstract]
ABSTRACT: In this paper, we introduce iterative schemes based on the extragradient method for finding a common element of the set of solutions of a generalized mixed equilibrium problem and the set of fixed points of a nonexpansive mapping, and the set of solutions of a variational inequality problem for inverse strongly monotone mapping. We obtain some strong convergence theorems for the sequences generated by these processes in Hilbert spaces. The results in this paper generalize, extend and unify some wellknown convergence theorems in literature.  [Show abstract] [Hide abstract]
ABSTRACT: In this paper, we introduce both explicit and implicit schemes for finding a common element in the common fixed point set of a oneparameter nonexpansive semigroup {T(s)0 ≤ s < ∞} and in the solution set of an equilibrium problems which is a solution of a certain optimization problem related to a strongly positive bounded linear operator. Strong convergence theorems are established in the framework of Hilbert spaces. As an application, we consider the optimization problem of a kstrict pseudocontraction mapping. The results presented improve and extend the corresponding results of many others. 2000 AMS Subject Classification: 47H09; 47J05; 47J20; 47J25.  [Show abstract] [Hide abstract]
ABSTRACT: In this paper, under the framework of real reflexive Banach space which admits a weakly sequentially continuous duality mapping from E to E∗, we study the strong convergence of an implicit and an explicit composite viscosity approximation algorithm (I) and (II), respectively for a pseudocontractive mapping T by using the weakly contractive mapping f as follows: (I)xt,s=tf(xt,s)+(1−t)yt,syt,s=sxt,s+(1−s)Txt,s and (II)xn+1=αnf(xn)+(1−αn)yn,yn=βnxn+(1−βn)Txn,n≥0. Our results unify, improve and complement several recent ones existing in the current literature.  [Show abstract] [Hide abstract]
ABSTRACT: In real reflexive separable Banach space which admits a weakly sequentially continuous duality mapping, the sufficient and necessary conditions that nonexpansive random selfmapping has a random fixed point are obtained. By introducing a random iteration process with weak contraction random operator, we obtain a convergence theorem of the random iteration process to a random fixed point for nonexpansive random selfmappings. 
Conference Paper: Random Approximation with Weak Contraction Random Operator and Random Fixed Point Theorem for Nonexpansive Random Mapping
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ABSTRACT: In real reflexive separable Banach space which admits a weakly sequentially continuous duality mapping, the sufficient and necessary condition that nonexpansive random mapping has a random fixed point is obtained. By introducing a random iteration process with weak contraction random operator, we obtain the convergence theorem of the random iteration process to a random fixed point for nonexpansive random mapping.  [Show abstract] [Hide abstract]
ABSTRACT: Let H be a Hilbert space and f a fixed contractive mapping with coefficient 0<α<1, A a strongly positive linear bounded operator with coefficient . Consider two iterative methods that generate the sequences {xn},{yn} by the algorithm, respectively. (I)(II) where {αn} and {tn} are two sequences satisfying certain conditions, and ℑ={T(s):s≥0} is a oneparameter nonexpansive semigroup on H. It is proved that the sequences {xn},{yn} generated by the iterative method (I) and (II), respectively, converge strongly to a common fixed point x∗∈F(ℑ) which solves the variational inequality
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35  Citations  
7.48  Total Impact Points  
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Institutions

20092013

Hebei University of Science and Technology
Ch’inhuangtao, Hebei, China
