Abstract
AbstractIn this paper, we introduce and study iterative schemes for solving split equilibrium problems and fixed point problems of nonspreading multi-valued mappings in Hilbert spaces and prove that the modified Mann iteration converges weakly to a common solution of the considered problems. Moreover, we present some examples and numerical results for the main results.
Highlights
In the following, let H and H be real Hilbert spaces with the inner product ·, · and the norm ·
Since its inception by Blum and Oettli [ ] in, the equilibrium problem ( . ) has received much attention due to its applications in a large variety of problems arising in numerous problems in physics, optimizations, and economics
Liu [ ] introduced the following class of multi-valued mappings: a multivalued mapping T : C → CB(C) is said to be nonspreading if ux – uy ≤ ux – y + uy – x for some ux ∈ Tx and uy ∈ Ty for all x, y ∈ C. He proved a weak convergence theorem for finding a common element of the set of solutions of an equilibrium problem and the set of common fixed points
Summary
Let H and H be real Hilbert spaces with the inner product ·, · and the norm ·. The existence of fixed points and the convergence theorems of multi-valued mappings have been studied by many authors (see [ – ]).
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.
