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    STUDIA MATHEMATICA - Issue no. 4 / 2016  
         
  Article:   COUPLED FIXED POINT THEOREMS FOR RATIONAL TYPE CONTRACTIONS.

Authors:  GABRIELA PETRUŞEL.
 
       
         
  Abstract:   In this paper, we will consider the coupled fi xed problem in b-metric space for single-valued operators satisfying a generalized contraction condition of rational type. First part of the paper concerns with some fixed point theorems,while the second part presents a study of the solution set of the coupled fixed point problem. More precisely, we will present some existence and uniqueness theorems for the coupled fixed point problem, as well as a qualitative study of it (data dependence of the coupled fi xed point set, well-posedness, Ulam-Hyers stability and the limit shadowing property of the coupled fi xed point problem) under some rational type contraction assumptions on the mapping.

Mathematics Subject Classi fication (2010): 47H05, 47H09, 47H10.

Keywords: Fixed point, ordered metric space, rational type contraction, coupled fi xed point, data dependence, well-posedness, Ulam-Hyers stability, limit shad-owing property.
 
         
     
         
         
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