Affiliations: [a] Department of Mathematics, University of Management and Technology, Lahore, Pakistan
| [b] Department of Engineering Science, Bandırma Onyedi Eylül University, Bandırma, Balıkesir, Turkey
| [c] Research Institute for Natural Sciences, Hanyang University, Seoul, Korea
Correspondence:
[*]
Corresponding authors. Salman Furqan, Department of Mathematics, University of Management and Technology, Lahore, Pakistan. E-mail: [email protected] and Choonkil Park, Research Institute for Natural Sciences, Hanyang University, Seoul 04763, Korea. E-mail: [email protected].
Abstract: In this paper, we introduce the concept of fuzzy double controlled metric space that can be regarded as the generalization of fuzzy b-metric space, extended fuzzy b-metric space and controlled fuzzy metric space. We use two non-comparable functions α and β in the triangular inequality as:
Mq(x,z,tα(x,y)+sβ(y,z))≥Mq(x,y,t)∗Mq(y,z,s).
We prove Banach contraction principle in fuzzy double controlled metric space and generalize the Banach contraction principle in aforementioned spaces. We give some examples to support our main results. An application to existence and uniqueness of solution for an integral equation is also presented in this work.
