Abstract
AbstractThe purpose of this paper is to present a new iterative scheme for finding a common solution to a variational inclusion problem with a finite family of accretive operators and a modified system of variational inequalities in infinite-dimensional Banach spaces. Under mild conditions, a strong convergence theorem for approximating this common solution is proved. The methods in the paper are novel and different from those in the early and recent literature.
Highlights
1 Introduction Variational inequalities theory, which was introduced by Stampacchia [ ] in the early s, has emerged as an interesting and fascinating branch of applicable mathematics with a wide range of applications in industry, finance, economics, social, pure and applied sciences
Motivated and inspired by Zhang et al [ ], Qin et al [ ], López et al [ ], Takahashi et al [ ] and Khuangsatung and Kangtunyakarn [ ], we suggest and analyze a new iterative algorithm for finding a common solution to a variational inclusion problem with a finite family of accretive operators and a modified system of variational inequalities in infinite-dimensional Banach spaces
From ( . ), we introduce the combination of variational inclusion problems in Banach spaces as follows: find a point x∗ ∈ C such that λiAi + M x∗, i=
Summary
Variational inequalities theory, which was introduced by Stampacchia [ ] in the early s, has emerged as an interesting and fascinating branch of applicable mathematics with a wide range of applications in industry, finance, economics, social, pure and applied sciences. Let C be a nonempty closed convex subset of a real Banach space E. ([ ]) Let C be a nonempty closed convex subset of a real q-uniformly smooth Banach space E.
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.
