Topological Methods in Nonlinear Analysis

Absolute retractivity of the common fixed points set of two multifunctions

Hojat Afshari, Shahram Rezapour, and Naaser Shahzad

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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.

Article information

Source
Topol. Methods Nonlinear Anal., Volume 40, Number 2 (2012), 429-436.

Dates
First available in Project Euclid: 21 April 2016

Permanent link to this document
https://projecteuclid.org/euclid.tmna/1461259710

Mathematical Reviews number (MathSciNet)
MR3074474

Zentralblatt MATH identifier
1307.54037

Citation

Afshari, Hojat; Rezapour, Shahram; Shahzad, Naaser. Absolute retractivity of the common fixed points set of two multifunctions. Topol. Methods Nonlinear Anal. 40 (2012), no. 2, 429--436. https://projecteuclid.org/euclid.tmna/1461259710


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References

  • M.C. Alicu and O. Mark, Some properties of the fixed points set for multifunctions , Studia Univ. Babes-Bolyai Math., 25 (1980), 77–79 \ref\key 2
  • T. Lazar, D. O'Regan and A. Petrusel, Fixed points and homotopy results for Ciric-type multivalued operators on a set with two metrics , Bull. Korean Math. Soc., 45 (2008), 67–73 \ref\key 3
  • 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 \ref\key 4
  • H. Schirmer, Properties of the fixed point set of contractive multifunctions , Canad. Math. Bull., 13 (1970), 169–173 \ref\key 5
  • A. Sintamarian, A topological property of the common fixed points set of two multivalued operators , Nonlinear Anal., 70 (2009), 452–456 \ref\key 6 ––––, 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