On Bilateral Fuzzy Contractions

Abstract

Not long ago, a hybrid type of contraction called bilateral contraction is
introduced in the literature. Following this idea, in this paper, we initiate a novel type of contraction, known as bilateral fuzzy contraction, which combines two important results in fixed point theory. These are the Jaggi and Caristi type contractions. Our main motivation herein is to augment the literature by combining the aforementioned approaches, and thereby, extending and modifying these results from their crisp setting into the frame of fuzzy set theory. In support of the obtained results, a example is provided.