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STUDIA MATHEMATICA - Issue no. 4 / 2016 | |||||||
Article: |
COUPLED FIXED POINT THEOREMS FOR RATIONAL TYPE CONTRACTIONS. Authors: GABRIELA PETRUŞEL. |
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Abstract:
In this paper, we will consider the coupled fixed 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 fixed point set, well-posedness, Ulam-Hyers stability and the limit shadowing property of the coupled fixed point problem) under some rational type contraction assumptions on the mapping. Mathematics Subject Classification (2010): 47H05, 47H09, 47H10. Keywords: Fixed point, ordered metric space, rational type contraction, coupled fixed point, data dependence, well-posedness, Ulam-Hyers stability, limit shad-owing property.
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