We prove -convergence and strong convergence theorems of an iterative sequence generated by the Ishikawa’s method to a fixed point of a single-valued quasi-nonexpansive mappings in -uniformly convex metric spaces without assuming the metric convexity assumption. As a consequence of our single-valued version, we obtain a result for multi-valued mappings by showing that every multi-valued quasi-nonexpansive mapping taking compact values admits a quasi-nonexpansive selection whose fixed-point set of the selection is equal to the strict fixed-point set of the multi-valued mapping. In particular, we immediately obtain all of the convergence theorems of Laokul and Panyanak [Laokul, T.; Panyanak, B. A generalization of the inequality and its applications. Carpathian J. Math. 36 (2020), no. 1, 81–90] and we show that some of their assumptions are superfluous.
On convergence theorems for single-valued and multi-valued mappings in p-uniformly convex metric spaces
Puiwong, Jenjira and Saejung, Satit
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carpathian_2021_37_3_513_527Additional Information
Author(s) | Puiwong, Jenjira, Saejung, Satit |
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DOI | https://doi.org/10.37193/CJM.2021.03.13 |
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Authors
Abbas, Mujahid
Acu, Dumitru
Balaj, Mircea
Berinde, Mădălina
Berinde, Vasile
Bărbosu, Dan
Chidume, C. E.
Cho, Yeol Je
Choban, Mitrofan M.
Coroian, Iulian
Cosma, Ovidiu
Cristescu, Gabriela
Diudea, Mircea V.
Fukhar-ud-din, Hafiz
Gaidici, A.
Horvat-Marc, Andrei
Ioanoviciu, Aurel
Khan, Abdul Rahim
Kozma, Lidia Elena
Kumam, Poom
Lungu, Nicolaie
Marin, Marin
Megan, Mihail
Mortici, Cristinel
Mureșan, Anton S.
Mureșan, Viorica
Pişcoran, Laurian-Ioan
Pop, Adina
Pop, Maria Sânziana
Pop, Nicolae
Pop, Ovidiu T.
Pop, Petrică Claudiu
Pop, Vasile
Popa, Dorian
Popa, Valeriu
Pop Sitar, Corina
Păcurar, Mădălina
Păvăloiu, Ion
Rus, Ioan A.
Rusu, Cristian
Sass, Istvan Huba Attila
Suantai, Suthep
Tașcu, Ioana
Yao, Jen-Chih
Zelina, Ioana
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