Abstract
In this paper, we aim to construct a new strong convergence algorithm for a split common fixed point problem involving the demicontractive operators. It is proved that the vector sequence generated via the Halpern-like algorithm converges to a solution of the split common fixed point problem in norm. The main convergence results presented in this paper extend and improve some corresponding results announced recently. The highlights of this paper shed on the novel algorithm and the new analysis techniques.
Highlights
Let H1 and H2 be the Hilbert spaces and C and Q be nonempty closed and convex subsets of H1 and H2, respectively.e split feasibility problem (SFP) is known to find x ∈ C, such that Ax ∈ Q, (1)where A: H1 ⟶ H2 is a linear bounded operator
In [1], the split feasibility problem (SFP) in the finite-dimensional Hilbert spaces was introduced by Censor and Elfving. is problem is equivalent to a number of nonlinear optimization problems and finds numerous real applications, such as signal processing and medical imaging
In order to overcome the fault, Byrne [2, 8] proposed the following novel algorithm CQ, which is under the spotlight of recent research xn+1 PCxn − cA∗I − PQAxn, n ≥ 0, (3)
Summary
Let H1 and H2 be the Hilbert spaces and C and Q be nonempty closed and convex subsets of H1 and H2, respectively.e split feasibility problem (SFP) is known to find x ∈ C, such that Ax ∈ Q, (1)where A: H1 ⟶ H2 is a linear bounded operator. Is problem is equivalent to a number of nonlinear optimization problems and finds numerous real applications, such as signal processing and medical imaging (see, e.g., [2,3,4,5,6,7]) For this split problem, simultaneous multiprojections algorithm was employed by Censor and Elfving in the finitedimensional space Rn to obtain the algorithm as follows: xn+1 A− 1PQPA(C)Axn, (2). Where both C and Q are convex and closed subsets of Rn, the linear bounded operator A of Rn is an n × n matrix, and PQ is the orthogonal projection operator onto the sets Q. e above algorithm (2) involves the matrix A− 1 (one always assumes the existence of A− 1) at every iterative step. The approximate solutions of the SFP have been studied extensively by scholars and engineers (see, e.g., [9,10,11,12,13])
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callDisclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
