Common fixed point theorems for nonself-mappings in metrically convex spaces via altering distances

There exists extensive literature on fixed points of self-mappings in metric and Banach spaces. But in many applications the mappings under examination may not always be self-mappings, therefore fixed point theorems for nonself-mappings form a natural subject for investigation. Assad and Kirk [2] initiated the study of fixed point of nonselfmappings in metrically convex spaces. Indeed while doing so, Assad and Kirk [2] noticed that with some kind of metric convexity, domain and range of the mappings under examination can be considered of more varied type. In recent years, this technique due to Assad and Kirk [2] has been utilized by many researchers of this domain and by now there exists considerable literature on this topic. To mention a few, we cite [1, 2, 5, 6, 7, 8, 11, 12]. Recently, Assad [1] gave sufficient conditions for nonself-mappings defined on a closed subset of complete metrically convex metric spaces satisfying Kannan-type mappings [10] which have been currently generalized by M. S. Khan et al. [12]. For the sake of completeness, we state the main result of M. S. Khan et al. [12].