Strong Convergence of the Iterations of Quasi $phi$-nonexpansive Mappings and its Applications in Banach Spaces
نویسندگان
چکیده مقاله:
In this paper, we study the iterations of quasi $phi$-nonexpansive mappings and its applications in Banach spaces. At the first, we prove strong convergence of the sequence generated by the hybrid proximal point method to a common fixed point of a family of quasi $phi$-nonexpansive mappings. Then, we give applications of our main results in equilibrium problems.
منابع مشابه
Strong convergence of Halpern iterations for quasi-nonexpansive mappings and accretive operators in Banach spaces
In this paper, we first introduce a new Halpern-type iterative scheme to approximate common fixed points of an infinite family of quasi-nonexpansive mappings and obtain a strongly convergent iterative sequence to the common fixed points of these mappings in a uniformly convex Banach space. We then apply our method to approximate zeros of an infinite family of accretive operators and derive a st...
متن کاملStrong Convergence of Cesàro Mean Iterations for Nonexpansive Nonself-Mappings in Banach Spaces
Let E be a real uniformly convex Banach space which admits a weakly sequentially continuous duality mapping from E to E∗, C a nonempty closed convex subset of E which is also a sunny nonexpansive retract of E, and T : C→ E a non-expansive nonself-mapping with F(T) = ∅. In this paper, we study the strong convergence of two sequences generated by xn+1 = αnx + (1− αn)(1/n+ 1) ∑n j=0(PT) xn and yn+...
متن کاملConvergence theorems of implicit iterates with errors for generalized asymptotically quasi-nonexpansive mappings in Banach spaces
In this paper, we prove that an implicit iterative process with er-rors converges strongly to a common xed point for a nite family of generalizedasymptotically quasi-nonexpansive mappings on unbounded sets in a uniformlyconvex Banach space. Our results unify, improve and generalize the correspond-ing results of Ud-din and Khan [4], Sun [21], Wittman [23], Xu and Ori [26] andmany others.
متن کاملWeak and Strong Convergence for Quasi-nonexpansive Mappings in Banach Spaces
In this paper, we first show that the iteration {xn} defined by xn+1 = P ((1−αn)xn +αnTP [βnTxn + (1− βn)xn]) converges strongly to some fixed point of T when E is a real uniformly convex Banach space and T is a quasi-nonexpansive non-self mapping satisfying Condition A, which generalizes the result due to Shahzad [11]. Next, we show the strong convergence of the Mann iteration process with err...
متن کاملStrong Convergence Theorems for Bregman Quasi–asymptotically Nonexpansive Mappings and Equilibrium Problem in Reflexive Banach Spaces
The purpose of this article is to propose an iteration algorithm for Bergman quasiasymptotically nonexpansive mapping to have the strong convergence under a limit condition only in the framework of reflexive Banach spaces. As applications, we apply our results to a system of equilibrium problems. The results presented in the paper improve and extend the corresponding results of Reich and Sabach...
متن کاملStrong convergence theorems for equilibrium problems and quasi-φ-asymptotically nonexpansive mappings in Banach spaces
In this paper, we introduce two modified Mann-type iterative algorithms for finding a common element of the set of common fixed points of a family of quasi-φ-asymptotically nonexpansive mappings and the set of solutions of an equilibrium problem in Banach spaces. Then we study the strong convergence of the algorithms. Our results improve and extend the corresponding results announced by many ot...
متن کاملمنابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ذخیره در منابع من قبلا به منابع من ذحیره شده{@ msg_add @}
عنوان ژورنال
دوره 17 شماره 3
صفحات 71- 80
تاریخ انتشار 2020-07-01
با دنبال کردن یک ژورنال هنگامی که شماره جدید این ژورنال منتشر می شود به شما از طریق ایمیل اطلاع داده می شود.
میزبانی شده توسط پلتفرم ابری doprax.com
copyright © 2015-2023