Fixed point iteration for a countable family of multi-valued strictly pseudo-contractive-type mappings
نویسندگان
چکیده
This paper introduces a new averaged algorithm for finding a common fixed point of a countably infinite family of generalized k-strictly pseudocontractive multi-valued mappings. The new iterative sequence introduced is proved to be an approximating fixed point sequence for common fixed points of a countably infinite family of this class of mappings. Furthermore, under some mild assumptions, strong convergence theorems are also proved for this class of mappings. The method of proof used here is new and enables to overcome many strong restrictions appearing in contemporary literature. The stated theorems improve and generalize many recent works in iterative scheme for multi-valued mappings.
منابع مشابه
Some iterative algorithms for k-strictly pseudo-contractive mappings in a CAT (0) space
In this paper, we prove the ∆-convergence theorems of the cyclic algorithm and the new multi-step iteration for k-strictly pseudo-contractive mappings and give also the strong convergence theorem of the modified Halpern’s iteration for these mappings in a CAT (0) space. Our results extend and improve the corresponding recent results announced by many authors in the literature. Key–Words: CAT (0...
متن کاملIterative 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 کاملA new one-step iterative process for approximating common fixed points of a countable family of quasi-nonexpansive multi-valued mappings in CAT(0) spaces
In this paper, we propose a new one-step iterative process for a countable family of quasi-nonexpansive multi-valued mappings in a CAT(0) space. We also prove strong and $Delta$-convergence theorems of the proposed iterative process under some control conditions. Our main results extend and generalize many results in the literature.
متن کاملOn End and Coupled Endpoints of $theta$-$F$-Contractive Set-Valued Mappings
In this paper, we introduce a new concept in set-valued mappings which we have called condition $(UHS)$. Then, adding this condition to a new type of contractive set-valued mappings, recently has been introduced by Amini-Harandi [Fixed and coupled fixed points of a new type contractive set-valued mapping in complete metric spaces, Fixed point theory and applications, 215 (2012)], we prove that ...
متن کاملHierarchical fixed points of strictly pseudo contractive mappings for variational inequality problems
In this paper, we introduce a new iterative scheme that converges strongly to a common fixed point of a countable family of strictly pseudo-contractive mappings in a real Hilbert space which is also a solution of variational inequality problem related to quadratic minimization problems. Our results extend ones of Yao et al. [Math. and Comput. Modell. 52(9-10):1697-1705, 2010], Gu et al. [J. App...
متن کامل