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