Coincidence and common fixed points of integral contractions for L-fuzzy maps with applications in fuzzy functional inclusions

Article type: Research Article

Authors: Al Rawashdeh, Ahmed^a | Mehmood, Nayyar^{a; b; *} | Rashid, Maliha^b

Affiliations: [a] Department of Mathematical Sciences, College of Science, UAE University, Al Ain, UAE | [b] Department of Mathematics and Statistics, International Islamic University, H-10, Islamabad, Pakistan; Department of Mathematical Sciences, College of Science, UAE University, Al Ain, UAE

Correspondence: [*] Corresponding author. Nayyar Mehmood. E-mail: nayyarmaths@gmail.com.

Abstract: Branciari defined the integral contractions to generalize the Banach contraction principle. Moreover recently Phiangsungnoen proved a fixed point theorem to generalize the ordered structure and contractive conditions with admissible mappings. In this article, we prove some coincidence and common fixed point theorems for a pair of L-fuzzy mappings satisfying integral β-admissible and generalize integral contractions. These results generalize the above famous results and many others in the literature. We define two types of fuzzy functional inclusions and prove existence of their solutions as a consequence of our results. Some nontrivial examples are given to provide significance of ourresults.

Keywords: Integral contractions, L-fuzzy mappings, β - admissible , functional inclusions

DOI: 10.3233/JIFS-172155

Journal: Journal of Intelligent & Fuzzy Systems, vol. 35, no. 2, pp. 2173-2187, 2018