In this paper, we study fuzzy calculus in two main branches differential and integral.  Some rules for finding limit and $gH$-derivative of $gH$-difference, constant multiple of two fuzzy-valued functions are obtained and we also present fuzzy chain rule for calculating  $gH$-derivative of a composite function.  Two techniques namely,  Leibniz's rule and integration by parts are introduced for ...

in this paper, a vector version of the intermediate value theorem is established. the main theorem of this article can be considered as an improvement of the main results have been appeared in [textit{on fixed point theorems for monotone increasing vector valued mappings via scalarizing}, positivity, 19 (2) (2015) 333-340] with containing the uniqueness, convergent of each iteration to the fixe...

In this paper, a vector version of the intermediate value theorem is established. The main theorem of this article can be considered as an improvement of the main results have been appeared in [textit{On fixed point theorems for monotone increasing vector valued mappings via scalarizing}, Positivity, 19 (2) (2015) 333-340] with containing the uniqueness, convergent of each iteration to the fixe...

In this survey paper, we outline the proof of a recent differential intermediate value theorem for transseries. Transseries are a generalization of power series with real coefficients, in which one allows the recursive appearance of exponentials and logarithms. Denoting by T the field of transseries, the intermediate value theorem states that for any differential polynomials P with coefficients...

In the context of intuitionistic real analysis, we introduce the set F consisting of all continuous functions φ from [0, 1] to R such that φ(0) = 0 and φ(1) = 1. We let I0 be the set of all φ in F for which we may find x in [0, 1] such that φ(x) = 12 . It is well-known that there are functions in F that we can not prove to belong to I0, and that, with the help of Brouwer’s Continuity Principle ...