Geodesic
Existence and convergence results for a class of non-expansive type mappings in Banach spaces
Filomat, Tome 37 (2023) no. 4, p. 1187

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DOI

In this article, we concentrate on common fixed points of a pair of generalized non-expansive mappings, viz., generalized α-Reich-Suzuki non-expansive mappings. In this sequel, we introduce the three step Abbas-Nazir iterative algorithm for a pair of mappings. Then we obtain some results related to weak and strong convergence of sequences, satisfying this iterative algorithm, to obtain the common fixed points of two generalized α-Reich-Suzuki non-expansive mappings. Finally, we compare the convergence rate of our iteration technique to that of some well-known iteration techniques by some constructive numerical examples.
DOI : 10.2298/FIL2304187B
Classification : 47H10, 54H25
Keywords: Non-expansive mappings, common fixed points, uniformly convex Banach spaces, demiclosedness, weak convergence, Opial’s property, Fréchet differential norm 
Ashis Bera; Ankush Chanda; Lakshmi Kanta Dey; Hiranmoy Garai; Vladimir Rakočević. Existence and convergence results for a class of non-expansive type mappings in Banach spaces. Filomat, Tome 37 (2023) no. 4, p. 1187 . doi: 10.2298/FIL2304187B
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     author = {Ashis Bera and Ankush Chanda and Lakshmi Kanta Dey and Hiranmoy Garai and Vladimir Rako\v{c}evi\'c},
     title = {Existence and convergence results for a class of non-expansive type mappings in {Banach} spaces},
     journal = {Filomat},
     pages = {1187 },
     year = {2023},
     volume = {37},
     number = {4},
     doi = {10.2298/FIL2304187B},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/FIL2304187B/}
}
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