Common Fixed Point Theorems in Fuzzy Normed Space

Abstract

. Fixed point theory is an intriguing topic with numerous applications in several branches of mathematics. In addition, fixed point theory offers useful methods for problem-solving that may be used across many subfields of mathematical analysis. Fixed point theorems are concerned with mappings f of a set X into itself that, under particular conditions, permit a fixed point, that is, a point such that . In this paper, we use the triangle property on fuzzy normed space(Fn-space) to show a common fixed point (CF-point) without continuity. First, we review some of the fundamental terms used in the fuzzy context. After that the notion of triangle fuzzy norm is given then we show that the self mappings Γ and Λ have a CF-point in the setting of Fn-space. Additionally, certain applications of our main results to the Fredholm integral equation are investigated.