A Hybrid Iterative Algorithm for Fixed Point Approximation in CAT (0) Spaces
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Abstract
Fixed-point approximation in geodesic metric spaces is an important problem in nonlinear analysis and optimization. This study develops a hybrid iterative algorithm for approximating fixed points of total asymptotically nonexpansive mappings in CAT(0) spaces and establishes conditions for its strong convergence. The algorithm is formulated on a nonempty closed convex subset of a CAT(0) space and uses control parameters to generate successive approximations. The convergence analysis combines the geometric properties of CAT(0) spaces, particularly the CAT(0) convexity inequality, with the defining properties of total asymptotically nonexpansive mappings. Under suitable conditions on the control parameters and asymptotic error sequences, the generated sequence is proved to converge strongly to a fixed point of the underlying mapping. This result establishes a theoretical convergence guarantee for the proposed scheme and contributes to iterative fixed-point approximation in nonlinear metric spaces. The study also discusses the scheme’s limitations and outlines directions for further research, including extensions to other classes of nonlinear mappings and metric spaces and potential applications to optimization, variational inequalities, and equilibrium problems.
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References
Kadhim, A. J. (2021). New common fixed points for total asymptotically nonexpansive mapping in CAT(0) space. Baghdad Science Journal, 18(4), 1286–1293. https://doi.org/10.21123/bsj.2021.18.4.1286
Panwar, A., Lamba, P., & Kumar, S. (2022). Some convergence results using a new iterative algorithm in CAT(0) space. Results in Nonlinear Analysis, 5(3), 263–272. https://doi.org/10.53006/rna.1097678
Kumar, M., & Pathak, H. K. (2022). Numerical reckoning of fixed points for generalized nonexpansive mappings in CAT(0) spaces with applications. U.P.B. Scientific Bulletin, Series A, 84(2), 117–128.
Ali, F., Ali, J., & Nieto, J. J. (2020). Some observations on generalized non-expansive mappings with an application. Computational and Applied Mathematics, 39(2), Article 74. https://doi.org/10.1007/s40314-020-1101-4
Sanboonsiri, P., & Wongsasinchai, P. (2020). Generalized nonexpansive mappings in CAT(0) spaces. Progress in Applied Science and Technology, 10(1), 148–160. https://doi.org/10.14456/stj.2020.13
Nanjaras, B., & Panyanak, B. (2010). Demiclosed principle for asymptotically nonexpansive mappings in CAT(0) spaces. Fixed Point Theory and Applications, 2010, Article 268780. https://doi.org/10.1155/2010/268780
Niwongsa, Y., & Panyanak, B. (2010). Noor iterations for asymptotically nonexpansive mappings in CAT(0) spaces. International Journal of Mathematical Analysis, 4(13), 645–656.
Thakur, B. S., Thakur, D., & Postolache, M. (2015). Modified Picard-Mann hybrid iteration process for total asymptotically nonexpansive mappings. Fixed Point Theory and Applications, 2015, Article 140. https://doi.org/10.1186/s13663-015-0391-5
Pansuwan, A., & Sintunavarat, W. (2016). A new iterative scheme for numerical reckoning fixed points of total asymptotically nonexpansive mappings. Fixed Point Theory and Applications, 2016, Article 83. https://doi.org/10.1186/s13663-016-0573-9
Kumam, W., Pakkaranang, N., Kumam, P., & Cholamjiak, P. (2020). Convergence analysis of modified Picard-S hybrid iterative algorithms for total asymptotically nonexpansive mappings in Hadamard spaces. International Journal of Computer Mathematics, 97(1–2), 175–188. https://doi.org/10.1080/00207160.2018.1476685
Kadhim, A. J. (2022). Convergence theorems of three-step iteration algorithm in CAT(0) spaces. Iraqi Journal of Science, 63(4), 1642–1652. https://doi.org/10.24996/ijs.2022.63.4.22
Padcharoen, A., & Sukprasert, P. (2023). Convergence of iterative scheme for asymptotically nonexpansive mapping in Hadamard spaces. WSEAS Transactions on Mathematics, 22, 47–54. https://doi.org/10.37394/23206.2023.22.6
Verma, A., & Tripathi, B. P. (2023). Approximation of fixed points in CAT(0) spaces using a new three-step iteration process for asymptotically quasi-nonexpansive mapping. International Journal of Membrane Science and Technology, 10(4), 2577–2584. https://doi.org/10.15379/ijmst.v10i4.3677
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