By means of a kind of new idea, we consider  the $(in,ivq)$-fuzzy$h$-ideals of a hemiring.  First, the concepts of $(in,ivq)$-fuzzyleft(right) $h$-ideals of a hemiring are provided and some relatedproperties are investigated. Then, a kind  of quotient hemiring  ofa hemiring by an $(in,ivq)$-fuzzy $h$-ideal is presented andstudied. Moreover, the notions of generalized $varphi$-compatible$(in,ivq...

Let Lθ be the circular cone in IR which includes second-order cone as a special case. For any function f from IR to IR, one can define a corresponding vector-valued function fLθ on IR by applying f to the spectral values of the spectral decomposition of x ∈ IR with respect to Lθ. The main results of this paper are regarding the Hdifferentiability and calmness of circular cone function fLθ . Spe...

We construct two counter-examples related to Fréchet differentiability in infinite dimensions. The first one gives a convex Lipschitzian function on a Banach space such that its convolution with a given measure is Fréchet differentiable only on a measure zero set. The second one gives a Borel function on a space with a Gaussian measure such that it is Lipschitzian along the Cameron–Martin subsp...

Many dynamic systems can be modeled by fractional differential equations in which some external parameters occur under uncertainty. Although these increase the complexity, they present more acceptable solutions. With aid of Atangana-Baleanu-Caputo (ABC) operator, an advanced numerical-analysis approach is considered and applied this work to deal with different classes fuzzy integrodifferential ...

Abstract Extending the belongs to (∈) relation and quasi-coincidence with(q) relation between fuzzy points and a fuzzy subsets, the concept of (α, β)-fuzzy filters and (α, β)-fuzzy filters of lattice implication algebras are introduced, where α, β ∈ {∈h , qδ, ∈h ∨qδ, ∈h ∧qδ}, α, β ∈ {∈h, qδ, ∈h ∨ qδ, ∈h ∧ qδ} but α ∈h ∧qδ, α ∈h ∧ qδ, respectively, and some related properties are investigated. S...

For the eigenvalue function on symmetric matrices, we have gathered a number of it’s properties.We show that this map has the properties of continuity, strict continuity, directional differentiability, Frechet differentiability, continuous  differentiability. Eigenvalue function will be extended to a larger set of matrices and then the listed properties will prove again.

In Kirchheim-Magnani [7] the authors construct a left invariant distance ρ on the Heisenberg group such that the identity map id is 1-Lipschitz but it is not metrically differentiable anywhere. In this short note we give an interpretation of the Kirchheim-Magnani counterexample to metric differentiability. In fact we show that they construct something which fails shortly from being a dilatation...