Fixed point theorems for contractions in complete \(E\)-fuzzy metric spaces

Abstract

Many problems in mathematics are to find fixed point of the mapping \(T:X\rightarrow X\), that is \(T(x)=x\) and to study the existence and uniqueness of these points. These results are applied in differential and integral equations. Because of this, many authors proved existence and uniqueness of fixed point of mappings under some contractions in different spaces. The aim of this paper is to study some fixed point theorems for contractions in complete \(E\)-fuzzy metric spaces by using \(\psi\) function and \(\phi\) function. The uniqueness and continuity of this fixed point is studied. Also an example is given to illustrate the main theorem and presented some applications in integral equations of obtained results. The theorems in this study generalized some well-known comparable results and introduced a novel approach to show the existence and uniqueness of solution of integral equations.