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Fixed point theorems for convex minimization problems in complex valued CAT(0) spaces. (English) Zbl 1481.54054

Summary: In this paper, we introduce the concept of a complex valued CAT(0) space and propose a new proximal point algorithm for certain nonlinear operators satisfying rational expressions in the framework of complex valued CAT(0) spaces. We prove existence of fixed point of these nonlinear mappings in such spaces and we prove strong and \(\Delta\)-convergence of the iterative sequence generated through our proposed algorithm to the minimizer of a convex function and the fixed point of these mappings. We show that the new iterative algorithm converges faster than the modified Mann-type and Ishikawa-type proximal point algorithms.

MSC:

54H25 Fixed-point and coincidence theorems (topological aspects)
54E40 Special maps on metric spaces
54E50 Complete metric spaces
65J15 Numerical solutions to equations with nonlinear operators
90C25 Convex programming
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