Absolute retractivity of the common fixed points set of two multifunctions

Hojat Afshari, Shahram Rezapour, Naseer Shahzad

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.

Keywords


Absolute retract; common fixed point; multifunction

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