Abstract
In this paper, we present a new iterative scheme for finding a common element of the solution set F of the split feasibility problem and the fixed point set F ( T ) of a right Bregman strongly quasi-nonexpansive mapping T in p-uniformly convex Banach spaces which are also uniformly smooth. We prove strong convergence theorem of the sequences generated by our scheme under some appropriate conditions in real p-uniformly convex and uniformly smooth Banach spaces. Furthermore, we give some examples and applications to illustrate our main results in this paper. Our results extend and improve the recent ones of some others in the literature.
Highlights
A Modified Iterative Algorithm for Split FeasibilityAnantachai Padcharoen 1,2 , Poom Kumam 1,2, *, Yeol Je Cho 3,4 and Phatiphat Thounthong 5,6
Let E1, E2 be Banach spaces and C, Q be nonempty closed convex subsets of E1 and E2, respectively.Let A: E1 → E2 be a bounded linear operator
In finite dimensional Hilbert spaces, the strong convergence of a sequence is equivalent to the weak convergence and the boundedness of a sequence implies that there exists a strongly
Summary
Anantachai Padcharoen 1,2 , Poom Kumam 1,2, *, Yeol Je Cho 3,4 and Phatiphat Thounthong 5,6. KMUTTFixed Point Research Laboratory, Department of Mathematics, Room SCL 802 Fixed Point. Laboratory, Science Laboratory Building, Faculty of Science, King Mongkut’s University of Technology. Thonburi (KMUTT), 126 Pracha-Uthit Road, Bang Mod, Thrung Khru, Bangkok 10140, Thailand. Received: 8 September 2016; Accepted: 1 November 2016; Published: 10 November 2016
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