Coupled coincidence point sets of $\alpha$-dominated mappings and stability analysis

Source abstract

In this paper we utilize a rational metric inequality for the purpose of establishing a coupled coincidence point theorem for a coupled mapping and a single-valued mapping on a metric space. We define some regularity condition on the mappings which are extensions of ideas involved in the well known admissibility condition. In the second part of the paper we make a stability analysis of the set of coupled coincidence points obtained here. All the main results are supported with illustrative examples. The work is in the domain of set valued analysis.