Strong Convergence Theorems for Variational Inequality Problems and a Countable Family of Total Quasi-φ-Asymptotically Nonexpansive Nonself Mappings
نویسندگان
چکیده
In this paper, we introduce an iterative process which converges strongly to a common element of solutions of variational inequality problems for γ-inverse strongly monotone mappings and common fixed points of a countable family of total quasi-φ-asymptotically nonexpansive nonself mappings, and hence obtain related convergence theorems in Banach spaces. Mathematics Subject Classification: 47H09; 47H05; 47J25
منابع مشابه
Iterative methods for finding nearest common fixed points of a countable family of quasi-Lipschitzian mappings
We prove a strong convergence result for a sequence generated by Halpern's type iteration for approximating a common fixed point of a countable family of quasi-Lipschitzian mappings in a real Hilbert space. Consequently, we apply our results to the problem of finding a common fixed point of asymptotically nonexpansive mappings, an equilibrium problem, and a variational inequality problem for co...
متن کاملStrong convergence theorems for a countable family of quasi-ϕ-asymptotically nonexpansive nonself mappings
In this paper, we introduce a class of total quasi-φ-asymptotically nonexpansive nonself mappings which contain several kinds of mappings as its special cases, and obtain some strong convergence theorems for this type of mappings in Banach spaces under some mild control conditions. The results presented in this paper improve and extend some recent corresponding results.
متن کاملWeak and strong convergence theorems for a finite family of generalized asymptotically quasinonexpansive nonself-mappings
In this paper, we introduce and study a new iterative scheme toapproximate a common xed point for a nite family of generalized asymptoticallyquasi-nonexpansive nonself-mappings in Banach spaces. Several strong and weakconvergence theorems of the proposed iteration are established. The main resultsobtained in this paper generalize and rene some known results in the currentliterature.
متن کاملStrong Convergence Theorems for a Countable Family of Total Quasi-φ-Asymptotically Nonexpansive Nonself Mappings
The purpose of this paper is to introduce a class of total quasi-φ-asymptotically nonexpansivenonself mappings and to study the strong convergence under a limit condition only in the framework of Banach spaces. As an application, we utilize our results to study the approximation problem of solution to a system of equilibrium problems. The results presented in the paper extend and improve the co...
متن کاملStrong Convergence of a Hybrid Projection Algorithm for Approximation of a Common Element of Three Sets in Banach Spaces
In this paper, we construct a new iterative scheme by hybrid projection method and prove strong convergence theorems for approximation of a common element of set of common fixed points of an infinite family of asymptotically quasi-φ-nonexpansive mappings, set of solutions to a variational inequality problem and set of common solutions to a system of generalized mixed equilibrium problems in a u...
متن کامل