A setvalued coupled coincidence point theorem with data dependence and weak stability results

Abstract

In this paper, we utilize an inequality involving a coupled multivalued mapping and a singlevalued mapping to obtain a coupled coincidence point theorem. We discuss special conditions under which coupled common fixed point theorems are obtained. The result combines together several ideas prevailing in fixed point theory related studies. There are several corollaries and an illustrative example. In the second part of the paper, we establish a multivalued coupled coincidence point result by putting together several ideas. A contraction through an implicit relation for the coupled mapping is assumed in the main theorem for quadruples of points determined by certain functions. The coupled mapping is also required to satisfy certain dominated conditions which are defined in this paper. In Secs. 3 and 4, we study the data dependence and stability of coupled coincidence point sets, respectively. For describing set distance we use the Hausdorff metric. The work is in the domain of setvalued analysis.