@Article{ATA-29-1,
author = {S. M. Ali},
title = {More on Fixed Point Theorem of $\{a,b,c\}$-Generalized Nonexpansive Mappings in Normed Spaces},
journal = {Analysis in Theory and Applications},
year = {2013},
volume = {29},
number = {1},
pages = {1--11},
abstract = {<p style="text-align: justify;">Let $X$ be a weakly Cauchy normed space in which the parallelogram law holds, $C$ be a bounded closed convex subset of $X$ with one contracting point and $T$ be an $\{a,b,c\}$-generalized-nonexpansive mapping from $C$ into $C$. We prove that the infimum of the set $\{\| x-T(x) \|\}$ on $C$ is zero, study some facts concerning the $\{a,b,c\}$-generalized-nonexpansive mapping and prove that the asymptotic center of any bounded sequence with respect to $C$ is singleton. Depending on the fact that the $\{a,b,0\}$-generalized-nonexpansive mapping from $C$ into $C$ has fixed points, accordingly, another version of the Browder&#39;s strong convergence theorem for mappings is given.</p>},
issn = {1573-8175},
doi = {https://doi.org/10.4208/ata.2013.v29.n1.1},
url = {http://global-sci.org/intro/article_detail/ata/4509.html}
}