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Proximal-type algorithms for split minimization problem in P-uniformly convex metric spaces. (English) Zbl 07128071

Summary: In this paper, we study strong convergence of some proximal-type algorithms to a solution of split minimization problem in complete \(p\)-uniformly convex metric spaces. We also analyse asymptotic behaviour of the sequence generated by Halpern-type proximal point algorithm and extend it to approximate a common solution of a finite family of minimization problems in the setting of complete \(p\)-uniformly convex metric spaces. Furthermore, numerical experiments of our algorithms in comparison with other algorithms are given to show the applicability of our results.

MSC:

47H09 Contraction-type mappings, nonexpansive mappings, \(A\)-proper mappings, etc.
47H10 Fixed-point theorems
49J20 Existence theories for optimal control problems involving partial differential equations
49J40 Variational inequalities

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