On minimization and fixed point problems in Hadamard spaces

Iterative approximation of common fixed points of two nonself asymptotically nonexpansive mappings in CAT(0) spaces with numerical examples

“…Note that every nonself asymptotically nonexpansive mapping with respect to P must be uniformly L-Lipschitzian with respect to P combined with (37), (47), and (50), where L = sup n∈N {k n } ≥ 1, we obtain…”

“…It is easy to see that (X, d X ) is a non-Hilbert CAT(0) spaces through the CN inequality (6). See, also, Salisu et al [37] and Eskandani and Raeisi [38]. Let r > 0, K ∶= {𝑦 ∈ X ∶ d X (𝑦, 0) ≤ r} and T 1 , T 2 ∶ K → X defined by…”

“…$$ It is easy to see that $$$ \left(X,{d}_X\right) $$$ is a non‐Hilbert CAT(0) spaces through the CN inequality (). See, also, Salisu et al [37] and Eskandani and Raeisi [38]. Let $$$ r>0,K:= \left\{y\in X:{d}_X\left(y,0\right)\le r\right\} $$$ and $$$ {T}_1,{T}_2:K\to X $$$ defined by $$$$ {T}_1\left({x}_1,{x}_2\right)=\left(2-{x}_1,{\left(2-{x}_1\right)}^2\right)\kern0.40em \mathrm{and}\kern0.40em {T}_2\left({x}_1,{x}_2\right)=\left(\frac{1}{2}\left(3-{x}_1\right),\frac{1}{4}{\left(3-{x}_1\right)}^2\right).$$…”

An Algorithm for Solving Pseudomonotone Variational Inequality Problems in CAT(0) Spaces

“…The theory of V.I.P. combines concepts of nonlinear operators and convex analysis in such a way that it generalizes both and is used to model nonlinear problems of physical phenomena in economics, sciences and engineering [3][4][5][6].…”

Golden ratio method for solving monotone variational inequality problems in Hadamard spaces

“…Moreover, our convergence result is established for mappings satisfying (3), which represents a less restrictive condition than the existing convergence results in the same setting. Our framework allows us to transform non-monotone (and non-convex) problems into monotone (convex) problems within the context of geodesic spaces [33][34][35]. To the best of our knowledge, this marks the first instance where problem (2) is considered within the framework of Hadamard spaces with the class of mappings satisfying the monotone type condition (3).…”