Abstract
AbstractOur main interest in this article is to introduce and study the class of θ-generalized demimetric mappings in Hadamard spaces. Also, a Halpern-type proximal point algorithm comprising this class of mappings and resolvents of monotone operators is proposed, and we prove that it converges strongly to a fixed point of a θ-generalized demimetric mapping and a common zero of a finite family of monotone operators in a Hadamard space. Furthermore, we apply the obtained results to solve a finite family of convex minimization problems, variational inequality problems and convex feasibility problems in Hadamard spaces.
Highlights
Let X be a metric space and C be a nonempty subset of X
A Halperntype proximal point algorithm (PPA) comprising this class of mappings and resolvents of monotone operators is proposed, and we prove that it converges strongly to a fixed point of a θ-generalized demimetric mapping and a common zero of a finite family of monotone operators in a Hadamard space
We apply the obtained results to solve a finite family of convex minimization problems, variational inequality problems (VIPs) and convex feasibility problems in Hadamard spaces
Summary
Let X be a metric space and C be a nonempty subset of X. They gave an example of a demimetric mapping and established some basic results for this class of mappings They proved a strong convergence theorem for approximating a fixed point of demimetric mappings and a solution to a minimization problem in Hadamard spaces. Motivated by the aforementioned results and the current interest in this research direction, we introduce and study the class of θ-generalized demimetric mappings in Hadamard spaces. A Halperntype PPA comprising this class of mappings and resolvents of monotone operators is proposed, and we prove that it converges strongly to a fixed point of a θ-generalized demimetric mapping and a common zero of a finite family of monotone operators in a Hadamard space. We apply the obtained results to solve a finite family of convex minimization problems, VIPs and convex feasibility problems in Hadamard spaces
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