Abstract:
The concepts of new classes of mappings are introduced in the spaces which
are more general space than the usual metric spaces. The obtained results are new and are
extension of Banach contraction principle. The existence and uniqueness of common fixed
points and fixed point results for the newly introduced classes of mappings are established
in the setting of complete complex valued b-metric spaces. An illustration is given by establishing the existence of solution of periodic differential equations in the framework of a
complete complex-valued b-metric spaces. The results obtained in this work provide extension as well as substantial generalization and improvement of several well-known results on
fixed point theory and its applications. The classes of mappings which are being considered
in this paper are more general and the results are obtained in more broad spaces.
