Fixed Points of $p$-Hybrid $L$-Fuzzy Contractions

Abstract

In this paper, the notion of $p$-hybrid $L$-fuzzy contractions in the framework of $b$-metric space is introduced. Sufficient conditions for existence of common $L$-fuzzy fixed points under such contractions are also investigated. The established ideas are generalizations of many concepts in fuzzy mathematics. In the case where our postulates are reduced to their classical variants, the concept presented herein merges and extends several significant and well-known fixed point theorems in the setting of both single-valued and multi-valued mappings in the corresponding literature of discrete and computational mathematics. A few of these special cases are pointed out and discussed. In support of our main hypotheses, a nontrivial example is provided.

Keywords

• $b$-metric space
• $l$-fuzzy set, $l$-fuzzy fixed point, $p$-hybrid $l$-fuzzy contraction, $l$-fuzzy set-valued map