Abstract
In this paper, we introduce two modified inertial hybrid and shrinking projection algorithms for solving fixed point problems by combining the modified inertial Mann algorithm with the projection algorithm. We establish strong convergence theorems under certain suitable conditions. Finally, our algorithms are applied to convex feasibility problem, variational inequality problem, and location theory. The algorithms and results presented in this paper can summarize and unify corresponding results previously known in this field.
Highlights
Throughout this paper, let C denote a nonempty closed convex subset of real Hilbert spaces H with standard inner products h·, ·i and induced norms k · k
The main purpose of this paper is to consider the following fixed point problem: Find x ∗ ∈ C, such that T ( x ∗ ) = x ∗, where T : C → C is nonexpansive with Fix( T ) 6= ∅
Inspired and motivated by the above works, in this paper, based on the modified inertial Mann algorithm (4) and the projection algorithm (2), we propose two new modified inertial hybrid and shrinking projection algorithms, respectively
Summary
Throughout this paper, let C denote a nonempty closed convex subset of real Hilbert spaces H with standard inner products h·, ·i and induced norms k · k. In 2003, Nakajo and Takahashi [17] established strong convergence of the Mann iteration with the aid of projections They considered the following algorithm: yn = αn xn + (1 − αn ) Txn ,. Very recently, inspired by the work of Sakurai and Iiduka [34], Dong et al [35] proposed a modified inertial Mann algorithm by combining the inertial method, the Picard algorithm and the conjugate gradient method. The iterative sequence { xn } defined by (4) converges weakly to a point in Fix( T ) under the following conditions:.
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.
