Abstract
We will introduce the concept ofn-tupled fixed points (for positive integern) in fuzzy metric space by mild modification of the concept ofn-tupled fixed points (for even positive intergern) introduced by Imdad et al. (2013) in metric spaces. As application of the above-mentioned concept, we will establish somen-tupled fixed point theorems for contractive type mappings in fuzzy metric space which extends the result of Roldán et al. (2013). Also we have given an application to solve a kind of Lipschitzian systems fornvariables and an integral system.
Highlights
The concept of coupled fixed point was introduced by Bhaskar and Lakshmikantham [1] and it motivated the fixed point theorists to work in the area of multidimensional fixed points; for example, see [2,3,4,5,6,7,8,9]
Imdad et al [9] introduced the concept of n-tupled coincidence points as well as n-tupled fixed point and utilize these two definitions to obtain n-tupled coincidence as well as n-tupled common fixed point theorems
The purpose of our results is to introduce n-tupled fixed points and to prove n-tupled fixed points theorems for contractive type mappings in fuzzy metric spaces
Summary
The concept of coupled fixed point was introduced by Bhaskar and Lakshmikantham [1] and it motivated the fixed point theorists to work in the area of multidimensional fixed points; for example, see [2,3,4,5,6,7,8,9].In recent years some of the fixed point theorists tried to establish the existence of n-tupled fixed points and common n-tupled fixed points for some contractions in metric spaces, partially ordered metric spaces and asymptotically regular metric spaces. Soliman et al [10] proved some n-tupled coincident point theorems in partially ordered complete asymptotically regular metric spaces. The purpose of our results is to introduce n-tupled fixed points (for all positive integers) and to prove n-tupled fixed points theorems for contractive type mappings in fuzzy metric spaces.
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