University of MaraghehSahand Communications in Mathematical Analysis2322-5807Articles in Press20210609Fixed Points of $p$-Hybrid $L$-Fuzzy Contractions24432510.22130/scma.2021.137899.863ENShehu ShagariMohammedDepartment of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria.0000-0002-0365-2878Ibrahim AliyuFulatanDepartment of Mathematics, Faculty of Physical Sciences, Ahmadu Bello University, Zaria, Nigeria.YahayaSirajoSchool of Arts and Sciences, American University of Nigeria, Yola, Adamawa State, Nigeria.Journal Article20201010In 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.