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The fixed point theory is a part of non-linear analysis since 1960 in the field of mathematics as it provides the necessary tools to have existence theorems in many different non-linear problems. Although Dutch mathematician L.E.J Brouwer established the first fixed point theorem but the credit of making concept useful and popular goes to Polish mathematician S. Banach in 1922 who proved famous Banach contraction mapping principle. The notion of dislocated metric space was first time introduced in 1986 under the name of metric domains. Dislocated quasi metric space was introduced in 2006 as a generalization of important theorems of dislocated metric space. These spaces are important extensions of metric space and play important roles for the development of non-linear analysis. This research work investigates some fixed point theorems in these spaces which extend and unify some well-known similar results in the literature. A survey work on some fixed point theorems of asymptotic contractions in metric space has also been presented. This work should be especially useful to young researchers and anyone else who work in the field of non linear analysis.


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