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    STUDIA MATHEMATICA - Issue no. 1 / 2014  
         
  Article:   A NOTE ON ZAMFIRESCU`S OPERATORS IN KASAHARA SPACES.

Authors:  ALEXANDRU-DARIUS FILIP.
 
       
         
  Abstract:   The aim of this paper is to give local and global fixed point results for Zamfirescu`s operators in Kasahara spaces. Since the domain invariance for Zamfirescu`s operators is not always satisfied, we use in our proofs the successive approximations method. Our local results extend and generalize Krasnoselskii`s local fixed point theorem by replacing the context of metric space with a more general one: the Kasahara space. On the other hand, instead of contractions we use Zamfirescu`s operators. As application, a homotopy result on large Kasahara spaces is given.

Mathematics Subject Classification (2010): 47H10, 54H25.

Keywords: Fixed point, Zamfirescu`s operator, Kasahara space, large Kasahara space, premetric, sequence of successive approximation.
 
         
     
         
         
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