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Generalized fixed point theorems on metric spaces

In this paper, we establish some fixed point theorems for single valued and multi-valued mappings on a complete metric space. Suzuki's and some other fixed point theorems are generalized by taking a more general contractive condition for single valued mappings. It is also proved that our result characterizes the completeness of the metric space. Further, taking generalized contractive condition, a fixed point theorem is also established for multi-valued mappings.