fixed point results for mapping satisfying rational inequality in complex valued metric spaces

In this paper we present some results of fixed point theory in a recently introduced generalizations of metric space, that is, complex valued metric space where the metric assumes value in the field of complex number. we assume a weak inequality with a rational expression in our theorem. the notion of inequality here is the order inequality in a partial ordering of the complex numbers. the results are illustrated with examples. the work is a part of the rapid extension of metric fixed point theory to more generalized structures beyond the boundary of metric spaces.