On θ-generalized demimetric mappings and monotone operators in Hadamard spaces

Abstract

Our 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.

Keywords

• θ-generalized demimetric mappings
• demimetric mappings
• monotone operators
• monotone inclusion problems
• hadamard spaces
• 47h09
• 47h10
• 49j20
• 49j40