Banach Contraction Principle (BCP) is a fundamental result in metric fixed point theory. It is a very powerful tool in solving the existence problems in pure and applied sciences. Also, The fuzzy set theory has much application in various branches of engineering and mathematical sciences including artificial intelligence, control engineering, computer science, management science etc.
The aim of this paper is to study a common fixed point results for fuzzy mappings under
implicit relation in a complex-valued metric space. we introduce new class of an implicit relation to prove a common fixed point theorems for fuzzy mappings in this paper. We construct examples to illustrate the main theorem. Further, we give the consequences of our main result.
Furthermore, the results have been reached in our current research work that consider applying for an integral type contractive condition.
The results presented in this paper extends some known results in this area.