Fixed point results and application for cyclic contractive maps in b-metric spaces

One of the generalizations of the usual metric function is b-metric, which allows the researchers a wider aria to derive many results and applications regarding the fixed point theory. This aim of the article is to advance new three fixed point principles in complete b-metric space instance is continuous function in two variables. Here, there are three directions to prove existence and uniqueness of fixed point. First, deriving a result in sense of Branciari’s theorem by combining integral contractive conditions with the idea of cyclic map. Second, applying the notion of cyclic representation regarding maps satisfying general weak conditions including an altering distance function to simulate the content of Boyd and Wong theorem. By this result, an application is given about the existence and uniqueness solution of an integral equation. Lastly, using an implicit relation with an altering distance function to construct cyclic contractive map. Furthermore, some examples are presented to analyze and illustrate the main results.