We introduced the notions of locally quasiconvex spaces and quasi-seminorms, and investigate the natural relationships between these two notions. As applications, we obtain generalizations of some well known , xed point theorems and , xed set theorems that require neither metrizability, nor compactness nor the standard notion of con-vexity.

In this paper, we investigate the estimation of fixed point errors for two important fixed point theorems of quasi-contractive mappings in fuzzy norm spaces. For this purpose, we define 􀀀generalized contraction and ("; )􀀀uniformly generalized contraction functions on fuzzy metric spaces and show that these definition are generalization of contractive functions defined by Ćirić on classical metric space. Also, when Picard’s iteration is used to approximate fixed points in fuzzy norm spaces, we obtain complete expressions for Ćirić’s fixed point theorems, including estimates of the fuzzy error.

In this paper we give some fixed point theorems in cone metric spaces and the purpose of this paper is the investigation of some manners for finding the fixed point of pointwise contraction and asymptotic pointwise contraction mappings.

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