In this paper, we solve two fixed point problems associated with the class of (c)-mappings. The first one is devoted to obtain the existence of fixed points for such mappings defined on \(\hbox {weak}^{\star }\) closed bounded convex subsets of duals of separable Banach spaces when the orthogonality relation \(\perp \) is uniformly \(\hbox {weak}^{\star }\) approximately symmetric. For the second problem, using the idea of R. Smarzewski (On firmly nonexpansive mappings, Proc. Am. Math. Soc 113(3):723–725,1991), we prove the existence of fixed points for such mappings which are defined on a finite union of weakly compact convex subsets of UCED (uniformly convex in every direction) Banach spaces.

中文翻译：

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Banach空间中（c）映射的一些不动点结果

在本文中，我们解决了与（c）映射类相关的两个不动点问题。第一个致力于获取当正交关系\（\ perp \时，在可分离Banach空间对偶的\（\ hbox {weak} ^ {\ star} \）封闭有界凸子集上定义的此类映射的不动点的存在。）统一\（\ hbox {weak} ^ {\ star} \）大致对称。对于第二个问题，使用R. Smarzewski的思想（关于牢固的非扩展映射，Proc。Am。Math。Soc 113（3）：723-725,1991），我们证明了已定义的此类映射的不动点的存在UCED（在每个方向上均匀凸）Banach空间的弱紧凸集的有限并集。