Viscosity approximation scheme for a family multivalued mapping
نویسنده
چکیده
Let K be a nonempty closed convex subset of a real reflexive Banach space X that has weakly sequentially continuous duality mapping Jφ for some gauge φ. Let Ti : K → K be a family of multivalued nonexpansive mappings with F := ∩∞i=0 F(Ti) ≠ ∅ which is a sunny nonexpansive retract of K with Q a nonexpansive retraction. It is our purpose in this paper to prove the convergence of two viscosity approximation schemes to a common fixed point x̄ = Qf (x̄) of a family of multivalued nonexpansive mappings in Banach spaces. Moreover, x̄ is the unique solution in F to a certain variational inequality. © 2011 Elsevier Ltd. All rights reserved.
منابع مشابه
Common fixed points of a finite family of multivalued quasi-nonexpansive mappings in uniformly convex Banach spaces
In this paper, we introduce a one-step iterative scheme for finding a common fixed point of a finite family of multivalued quasi-nonexpansive mappings in a real uniformly convex Banach space. We establish weak and strong convergence theorems of the propose iterative scheme under some appropriate conditions.
متن کاملConvergence theorems of iterative approximation for finding zeros of accretive operator and fixed points problems
In this paper we propose and studied a new composite iterative scheme with certain control con-ditions for viscosity approximation for a zero of accretive operator and xed points problems in areflexive Banach space with weakly continuous duality mapping. Strong convergence of the sequencefxng dened by the new introduced iterative sequence is proved. The main results improve andcomplement the co...
متن کاملA Slowness Matching Eulerian Method for Multivalued Solutions of Eikonal Equations
Traveltime, or geodesic distance, is locally the solution of the eikonal equation of geometric optics. However traveltime between sufficiently distant points is generically multivalued. Finite difference eikonal solvers approximate only the viscosity solution, which is the smallest value of the (multivalued) traveltime (‘‘first arrival time’’). The slowness matching method stitches together loc...
متن کاملBoundary Shear Stress in a Trapezoidal Channel
This paper focuses on a hydraulic radius separation approach used to calculate the boundary shear stress in terms of bed and wall shear stress proposed in a trapezoidal channel. The average bed and sidewall shear stress in smooth trapezoidal open channels are derived after using Guo & Julien (2005) early equations taking a part of an investigation to cover both rectangular and trapezoidal chann...
متن کاملA. Bunyawat and S. Suantai STRONG CONVERGENCE THEOREMS OF ONE-STEP ITERATIVE SCHEME FOR A COUNTABLE FAMILY OF MULTIVALUED MAPPINGS IN A BANACH SPACE
In this paper, we introduce a new one-step iterative scheme for finding a common fixed point of a countable family of multivalued mappings in a real uniformly convex Banach space. By using the best approximation operators, a necessary and sufficient condition for strong convergence of the proposed method is given. Moreover, we establish some strong convergence theorems of the proposed iterative...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
برای دانلود متن کامل این مقاله و بیش از 32 میلیون مقاله دیگر ابتدا ثبت نام کنید
ثبت ناماگر عضو سایت هستید لطفا وارد حساب کاربری خود شوید
ورودعنوان ژورنال:
- Mathematical and Computer Modelling
دوره 54 شماره
صفحات -
تاریخ انتشار 2011