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

Ogwo Grace N., Izuchukwu Chinedu, Aremu Kazeem O., Mewomo Oluwatosin T.

Demonstratio Mathematica

2020

Vol. 53, nr 1

95--111

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.