Abstract
A convergence theorem for approximating minimization and fixed point problems for non-self mappings in Hadamard spaces
Highlights
Let (X, d) be a metric space and x, y ∈ X
We say that a metric space X is a geodesic space if for every pair of points x, y ∈ X, there is a minimal geodesic from x to y
A geodesic space X is a CAT(0) space if the distance between an arbitrary pair of points on a geodesic triangle ∆ does not exceed the distance between its pair of corresponding points on its comparison triangle ∆ ̄
Summary
Let (X, d) be a metric space and x, y ∈ X. Zegeye and Tufa [50] proposed a new Halpern–Ishikawa type algorithm for approximating fixed points of non-self mappings without the use of metric projections or sunny nonexpansive retractions They proposed the following algorithm for an L-Lipschitz k-pseudocontractive mapping in a real Hilbert space: For an arbitrary x0 ∈ D, the sequence {xn} generated by λn ∈ [max{β, h(xn)}, 1), yn = λnxn ⊕ (1 − βn)T xn, θn ∈ [max{λn, l(yn)}, 1), xn+1 = αnu ⊕ (1 − αn)(θnxn + (1 − θn)T yn), n ≥ 0, converges to a fixed point of the multivalued hemicontractive mapping, where β ∈. Our proposed method improves and extends some recent works in the literature
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