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Paper   IPM / M / 15179
School of Mathematics
  Title:   The Reich-Zaslavski property and fixed points of non-self multivalued mappings
1.  Alireza Amini-Harandi
2.  Majid Fakhar (Joint with M. Goli and H. R. Hajisharifi)
  Status:   Published
  Journal: J. Fixed Point Theory Appl.
  Year:  2018
  Pages:   DOI: 10.1007/s11784-018-0511-z
  Supported by:  IPM
Let (X, d) be a metric space, Y be a nonempty subset of X, and let T : Y �?? P(X) be a non-self multivalued mapping. In this paper, by a new technique we study the fixed point theory of multivalued mappings under the assumption of the existence of a bounded sequence (xn)n in Y such that T nxn �?? Y, for each n �?? N. Our main result generalizes fixed point theorems due to Matkowski (Diss. Math. 127, 1975), W¸egrzyk (Diss. Math. (Rozprawy Mat.) 201, 1982), Reich and Zaslavski (Fixed Point Theory 8:303�??307, 2007), Petru¸sel et al. (SetValued Var. Anal. 23:223�??237, 2015) and provides a solution to the problems posed in Petru¸sel et al. (Set-Valued Var. Anal. 23:223�??237, 2015) and Rus and S¸erban (Miskolc Math. Notes 17:1021�??1031, 2016).

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