Absolute retractivity of the common fixed points set of two multifunctions

Abstract

In 1970, Schirmer discussed about topological properties of the fixed point set of multifunctions ([< i> Properties of the fixed point set of contractive multifunctions< /i> , Canad. Math. Bull. < b> 13< /b> (1970), 169-173]). Later, some authors continued this study by providing different conditions ([M.C. Alicu and O. Mark, < i> Some properties of the fixed points set for multifunctions< /i> , Studia Univ. Babes-Bolyai Math. < b> 25< /b> (1980), 77-79] and [B. Ricceri, < i> Une propriete topologique de l'ensemble des points fixes d'une contraction multivoque a valeurs convexes< /i> , Atti. Acc. Lincei Rend. < b> 81< /b> (1987), 283-286]). Recently, Sintamarian proved results on absolute retractivity of the common fixed points set of two multivalued operators ([< i> A topological property of the common fixed points set of two multivalued operators< /i> , Nonlinear Anal. < b> 70< /b> (2009), 452-456] and [< i> A topological property of the common fixed points set of two multivalued operators satisfying a Latif-Beg type condition< /i> , Fixed Point Theory < b> 9< /b> (2008), 561-573]). We shall present some results on absolute retractivity of the common fixed points set of two multifunctions by using different conditions.