Abstract
In this paper, we propose a new algorithm for solving the split common fixed point problem for infinite families of demicontractive mappings. Strong convergence of the proposed method is established under suitable control conditions. We apply our main results to study the split common null point problem, the split variational inequality problem, and the split equilibrium problem in the framework of a real Hilbert space. A numerical example supporting our main result is also given.
Highlights
Let H be a real Hilbert space with inner product ·, · and norm ·
The multiple set split feasibility problem (MSSFP), which was first introduced by Censor et al [4], is to find m r v∗ ∈ Ci such that Av∗ ∈ Qi, (4)
We introduce a new algorithm for solving problem (7) for infinite families of demicontractive mappings and prove its strong convergence to a solution of problem (7)
Summary
Let H be a real Hilbert space with inner product ·, · and norm ·. Let C and Q be nonempty closed convex subsets of real Hilbert spaces H1 and H2, respectively. The split common fixed point problem (SCFP) for mappings T and S, which was first introduced by Censor and Segal [5], is to find v∗ ∈ F(T) such that Av∗ ∈ F(S),. Where A1, A2 : H1 → H2 are bounded linear operators, and {Ui : H1 → H1 : i ∈ N}, {Ti : H2 → H2 : i ∈ N} and {Si : H2 → H2 : i ∈ N} are infinite families of k3-, k2-, and k1demicontractive mappings, respectively. We introduce a new algorithm for solving problem (7) for infinite families of demicontractive mappings and prove its strong convergence to a solution of problem (7)
Sign-in/Register to view highlights & summary 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.
