Fixed point problem of a multi-valued Kannan-Geraghty type contraction via w-distance

Combining certain existing concepts we define a new multi-valued contraction with respect to w-distance. The underline metric space is assumed to have a relation defined on it. We prove the existence of non-null fixed point sets for these mappings under appropriate assumptions. The uniqueness of the fixed point is proved separately under some additional conditions. We also discuss Hyers-Ulam-Rassias stability and well-posedness property of the fixed point problem. For that purpose we formulate them here in terms of w-distance. There are several corollaries, illustrative examples and remarks. Some existing results are shown to be extended by our result. The study is in the domain of multi-valued relational fixed point theory with w-distance.