On Fixed Point Results of L-Fuzzy Set-Valued Maps

Subject Areas : International Journal of Mathematical Modelling & Computations

Shehu Shagari Mohammed ¹ , Iqra Zia ² , Akbar Azam ³

1 - Department of Mathematics, Ahmadu Bello University
2 - Department of Mathematics, COMSATS University, Chak Shahzad, Islamabad,44000, Pakistan
3 - Department of Mathematics, COMSATS University, Chak Shahzad, Islamabad,44000, Pakistan

Received: 2020-09-20 Accepted : 2021-04-30 Published : 2021-06-20

Keywords: fixed point, fuzzy set, Fuzzy mapping, L-fuzzy set, L-fuzzy mapping, multivalued map,

Abstract :

In this paper, two novel extensions of Banach and Meir-Keeler fixed point theorems for $L$-fuzzy set-valued map defined on a complete metric space are presented by using new general contractive conditions under suitable assumptions. In the case when the $L$-fuzzy set-valued map is reduced to its crisp counterparts, our obtained concepts herein generalize several significant fixed point theorems of point-to-point and point-to-set valued mappings in the comparable literature. We provide non-trivial examples to validate the hypotheses of our results.