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The purpose of this paper is to study the coupled fixed point problem and the coupled best proximity problem for single-valued and multi-valued contraction type operators defined on cyclic representations of the space. The approach is based on fixed point results for appropriate operators generated by the initial problems. [ABSTRACT FROM AUTHOR]

In this paper we present some important generalizations of the Banach contraction principle in which the Lipschitz constant k is replaced by some real-valued control function. For the applications to the fractal, we obtain the fixed point theorem of the some generalized contraction in the fractal space. [ABSTRACT FROM AUTHOR]

In this paper, we prove that every intuitionistic fuzzy metric space has a basis that is countably locally finite. We use this result to conclude that every intuitionistic fuzzy metric space is metrizable. We also introduce notions of orbitally complete intuitionistic fuzzy metric spaces and generalized contraction mappings, and prove fixed point theorems which are extensions of the classical Banach's fixed point principle and fixed point theorems of Edelstein [4] and Grabiec [7]. Our results also extend, generalize and fuzzify several fixed point theorems on metric spaces, Menger probabilistic metric spaces, uniform spaces and fuzzy metric spaces. [ABSTRACT FROM AUTHOR]

In this paper, we prove that every intuitionistic fuzzy metric space has a basis that is countably locally finite. We use this result to conclude that every intuitionistic fuzzy metric space is metrizable. We also introduce notions of orbitally complete intuitionistic fuzzy metric spaces and generalized contraction mappings, and prove fixed point theorems which are extensions of the classical Banach's fixed point principle and fixed point theorems of Edelstein [4] and Grabiec [7]. Our results also extend, generalize and fuzzify several fixed point theorems on metric spaces, Menger probabilistic metric spaces, uniform spaces and fuzzy metric spaces. [ABSTRACT FROM AUTHOR]