A quasitoric manifold (resp. a small cover) is a 2ndimensional (resp. an n-dimensional) smooth closed manifold with an effective locally standard action of (S) (resp. (Z2)n) whose orbit space is combinatorially an n-dimensional simple convex polytope P . In this paper we study them when P is a product of simplices. A generalized Bott tower over F, where F = C or R, is a sequence of projective b...

We collect the recent results on invariant f -structures in the generalized Hermitian geometry. Here the canonical f -structures on homogeneous k-symmetric spaces play a remarkable role. Specifically, these structures provide a wealth of invariant examples for the classes of nearly Kähler f -structures, Hermitian f -structures and some others. Finally, we consider all invariant f structures on ...

Chmieliński has proved in the paper [4] the superstability of the generalized orthogonality equation |〈 f (x), f (y)〉| = |〈x,y〉|. In this paper, we will extend the result of Chmieliński by proving a theorem: Let Dn be a suitable subset of Rn. If a function f : Dn → Rn satisfies the inequality ||〈 f (x), f (y)〉|− |〈x,y〉|| ≤ φ(x,y) for an appropriate control function φ(x,y) and for all x,y ∈ Dn, ...

The generalized Kähler structures were introduced and studied by M. Gualtieri in his PhD thesis [16] in the more general context of generalized geometry started by N. Hitchin in [20]. There are many explicit constructions of non-trivial generalized-Kähler structures [1, 2, 21, 24, 25, 4, 7]. For instance Gualtieri proved that all compact-even dimensional semisimple Lie groups are generalized Kä...

In this paper, using the fixed point and direct methods, we prove the generalized Hyers-Ulam-Rassias stability of the following Cauchy-Jensen additive functional equation: begin{equation}label{main} fleft(frac{x+y+z}{2}right)+fleft(frac{x-y+z}{2}right)=f(x)+f(z)end{equation} in various normed spaces. The concept of Hyers-Ulam-Rassias stability originated from Th. M. Rassias’ stability theorem t...

The main purpose of this paper is to establish some new results onthe superstability and stability via a fixed point approach forthe Pexiderized exponential equation, i.e.,$$|f(x+y)-g(x)h(y)|leq psi(x,y),$$where $f$, $g$ and $h$ are three functions from an arbitrarycommutative semigroup $S$ to an arbitrary unitary complex Banachalgebra and also $psi: S^{2}rightarrow [0,infty)$ is afunction. Fur...

Let φ and ψ be analytic self-maps of the open unit disk D . Using pseudo-hyperbolic distance ρ(φ ,ψ) , we characterize the boundedness and compactness of the differences of generalized composition operators (C φ −Ch ψ ) f (z) = ∫ z 0 [ f ′(φ(ξ ))g(ξ )− f ′(ψ(ξ ))h(ξ )]dξ , z ∈ D between two Bloch-type spaces on D . The results generalize the corresponding results on the single generalized compo...

*Correspondence: [email protected] Chung-Jen Junior College of Nursing, Health Sciences and Management, Dalin, 62241, Taiwan Abstract In this paper, we establish sufficient optimality conditions for the (weak) efficiency to multiobjective fractional programming problems involving generalized (F,α,ρ ,d)-V-type I functions. Using the optimality conditions, we also investigate a parametric-type dua...

The (2, F) generalized Fibonacci sequences were defined in [1] and [2]. In [3] K. Atanassov extended the definition to the case of three sequences and listed thirty-six systems defining the (3, F) generalized Fibonacci sequences. Ten of these thirty-six systems were discarded as trivial and the remaining twenty-six were placed in seven classes termed "groups." In this paper the structure of the...