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

A New Generalization of Rhoades' Condition