A modular space Xρ is defined by a corresponding modular ρ, that is, Xρ = {x ∈ X : ρ(λx) → 0 as λ → 0}. Based on definition of the modular space, Kozłowski [3, 4] introduced the notion ofmodular… (More)

In this paper, several similarity measures of fuzzy soft sets are introduced based on four types of fuzzy quasi-metrics. Meantime, an illustrative example is also given.

In this paper, we establish the general solution of a new quadratic functional equation f ( x− y+z 2 ) + f ( x+ y−z 2 ) + f(x+ z) = 3f(x) + 12f(y) + 3 2f(z). Next, the Ulam stability of this equation… (More)

Algebraic method is one of important ways in the study of rough sets theory. One may profoundly understand the algebraic structure of approximation operator through this method research. In this… (More)

Using the integrating factor method, this paper deals with the Hyers-Ulam stability of a class of exact differential equations of second order. As a direct application of the main result, we also… (More)

In this paper, we prove the Ulam stability of the following set-valued functional equation by employing the direct method and the fixed point method, respectively, f ( x− y + z 2 ) ⊕ f ( x+ y − z 2 )… (More)

and Applied Analysis 3 Definition 2.2 Kramosil and Michálek 3 . The triple X,M, ∗ is called a fuzzy metric space if X is an arbitrary set, ∗ is a continuous t-norm, andM is a fuzzy set onX×X× 0,∞… (More)