A New Generalization of Rhoades' Condition.

In this paper, our aim is to obtain a new generalization of the well-kown Rhoades' contractive condition. To do this, we introduce the notion of an $S$-normed space. We extend the Rhoades' contractive condition to $S$-normed spaces and define a new type of contractive conditions. We support our theoretical results with necessary illustrative examples.