FIXED POINT AND EXTENDED COUPLED FIXED POINT THEOREMS FOR MULTI-VALUED CONTRACTIONS WITH RESPECT TO THE POMPEIU FUNCTIONAL

摘要

In this paper, we will prove some fixed point results using a Pompeiu type metric on P-cl (X), for multi-valued operators satisfying two conditions: contractivity and monotonicity. The approach is based on a fixed point theorem for a multi-valued operator in the setting of a b-metric space. Several qualitative properties(well-posedness, Ulam-Hyers stability) are also obtained. In the second part of this paper, we will consider the extended coupled fixed point problem for a multi-valued operator. We will consider the problem of the existence of the solutions. Data dependence and well-posedness of the extended coupled fixed point problem are also discussed.