arXiv subjects
Publications and source records attributed to M. R. Alfuraidan.
In this paper, we introduce the concept of monotone Gregus-Ćirić-contraction mappings in weighted digraphs. Then we establish a fixed point theorem for monotone Gregus-Ćirić-contraction mappings defined in convex weighted digraphs.
Let $(X,\|.\|)$ be a Banach space. Let $C$ be a nonempty, bounded, closed, and convex subset of $X$ and $T: C \rightarrow C$ be a $G$-monotone nonexpansive mapping. In this work, it is shown that the Mann iteration sequence defined by $$x_{n+1} = t_n T(x_n) + (1-t_n)x_n, \, n = 1, 2, \cdots$$ can be proved the existence of a fixed point of $G$-monotone nonexpansive mappings.
In this work, we define the concept of mixed $G$-monotone mappings defined on a metric space endowed with a graph. Then we obtain sufficient conditions for the existence of coupled fixed points for such mappings when a weak contractivity type condition is satisfied.