In this paper‎, ‎the existence and uniqueness of the ‎solution of a nonlinear fully fuzzy implicit integro-differential equation‎ ‎arising in the field of fluid mechanics is investigated. ‎First,‎ an equivalency lemma ‎is ‎presented ‎by‎ which the problem understudy ‎is ‎converted‎ to ‎the‎ two different forms of integral equation depending on the kind of differentiability of the solution. Then...

In this paper, we introduce the cone normed spaces and cone bounded linear mappings. Among other things, we prove the Baire category theorem and the Banach--Steinhaus theorem in cone normed spaces.

In the existing literature, Banach contraction theorem as well Meir-Keeler fixed point were extended to fuzzy metric spaces. However, extensions require strong additional assumptions. The purpose of this paper is determine a class spaces in which both theorems remain true without need any condition. We demonstrate wide validity new class.

The fuzzy differential and integral equations are important part of the fuzzy analysis theory and they have the important value of theory and application in control theory. Seikkala in [8] has defined the fuzzy derivative which is the generalization of the Hukuhara derivative in [7], the fuzzy integral which is the same as that of Dubois and prade [1], and by means of the extension principle of...

The aim of this paper is to introduce and solve the generalized radical cubic functional equation related to quadratic functional equation$$fleft(sqrt[3]{ax^{3}+by^{3}}right)+fleft(sqrt[3]{ax^{3}-by^{3}}right)=2a^{2}f(x)+2b^{2}f(y),;; x,yinmathbb{R},$$for a mapping $f$ from $mathbb{R}$ into a vector space. We also investigate some stability and hyperstability results for...

The notion of regularity in a Banach algebra was introduced and studied in [KM] and [MM]. A non-empty subset R of a unital Banach algebra A is called a regularity if it satisfies the following two conditions: (i) if a ∈ A and n ∈ N, then a ∈ R ⇔ a ∈ R, (ii) if a, b, c, d are mutually commuting elements of A satisfying ac + bd = 1A then ab ∈ R ⇔ a, b ∈ R. The axioms of regularities are weak enou...

This paper presents a formal proof of the Riesz representation theorem in the PVS theorem prover. The Riemann Stieltjes integral was defined in PVS, and the theorem relies on this integral. In order to prove the Riesz representation theorem, it was necessary to prove that continuous functions on a closed interval are Riemann Stieltjes integrable with respect to any function of bounded variation...

In this paper we prove that a transitive fuzzy relation R on a set X can be extended to a total transitive fuzzy relation Q on X preserving the irreflexivity of R. This generalizes a classical theorem of Szpilrajn that asserts that any strict order on X can be extended to a total strict order on X . The extension theorem that we obtain will be used in the fuzzy analysis of a classical Richter t...