New fixed point results of the sum of two operators in fuzzy metric spaces and their applications

In the fuzzy fixed point theory literature, discussions of fixed points have been limited to maps involving a single function. Till now, the presence of a fixed point for the sum of two fuzzy operators is an open question, and in our study, we have affirmatively answered that question. The paper is primarily concerned with the solution of the operator equation, where one of the operators is a fuzzy compact linear operator and the other is a variety of contraction and contractive maps. At the end, we apply the main findings to an integral equation.