Abstract
In this note, we propose one proposition and two examples to answer completely an open question on the approximate fixed point sequence of \((\alpha ,\beta )\)-maps.
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Amini-Harandi, A., Fakhar, M., Hajisharifi, H.R.: Approximate fixed points of \(\alpha \)-nonexpansive mappings. J. Math. Anal. Appl. 467(2), 1168–1173 (2018)
Aoyama, K., Kohsaka, F.: Fixed point theorem for \(\alpha \)-nonexpansive mappings in Banach spaces. Nonlinear Anal. 74(13), 4387–4391 (2011)
Chang, S.-S., Wang, L., Wang, X.R., Zhao, L.C.: Common solution for a finite family of minimization problem and fixed point problem for a pair of demicontractive mappings in Hadamard spaces. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 114(2), 12 (2020). (Paper No. 61)
Cho, Y.J.: Survey on metric fixed point theory and applications. In: Advances in Real and Complex Analysis with Applications, pp. 183–241. Springer, Berlin (2017)
Jailoka, P., Suantai, S.: The split common fixed point problem for multivalued demicontractive mappings and its applications. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 113(2), 689–706 (2019)
Kirk, W., Shahzad, N.: Fixed Point Theory in Distance Spaces. Springer, Cham (2014)
Pakkaranang, N., Kumam, P., Cho, Y.J.: Proximal point algorithms for solving convex minimization problem and common fixed points problem of asymptotically quasi-nonexpansive mappings in \(cat(0)\) spaces with convergence analysis. Numer. Algor. 78(3), 827–845 (2018)
Pant, R., Shukla, R.: Approximating fixed points of generalized \(\alpha \)-nonexpansive mappings in Banach spaces. Numer. Funct. Anal. Optim. 38(2), 248–266 (2017)
Pant, R., Shukla, R., Rakočević, V.: Approximating best proximity points for Reich type non-self nonexpansive mappings. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 114(4), 14 (2020). (Paper No. 197)
Song, Y., Muangchoo-In, K., Kumam, P., Cho, Y.J.: Successive approximations for common fixed points of a family of \(\alpha \)-nonexpansive mappings. J. Fixed Point Theory Appl. 20(1), 13 (2018). (Paper No. 10)
Suparatulatorn, R., Cholamjiak, P., Suantai, S.: Self-adaptive algorithms with inertial effects for solving the split problem of the demicontractive operators. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 114(1), 16 (2020). (Paper No. 40)
Suparatulatorn, R., Suantai, S., Phudolsitthiphat, N.: Reckoning solution of split common fixed point problems by using inertial self-adaptive algorithms. Rev. R. Acad. Cienc. Exactas Fís. Nat. Ser. A Mat. RACSAM 113(4), 3101–3114 (2019)
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The authors would like to thank the reviewers for many valuable comments to revise the paper much better.
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Van Dung, N., Radenovic, S. Remarks on the approximate fixed point sequence of \((\alpha ,\beta )\)-maps. Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. 115, 193 (2021). https://doi.org/10.1007/s13398-021-01142-z
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DOI: https://doi.org/10.1007/s13398-021-01142-z