Volume 45, Issue 4

In this paper the definition of fuzzy antinorm is modified. Some properties of finite dimensional fuzzy antinormed linear space are studied. Fuzzy α -anti-convergence and fuzzy α -anti-complete linear spaces are defined and some of their properties are studied.

Necessary and sufficient conditions will be found for quadruples of lattices to be isomorphic to lattices of weak, relative, strong subalgebras and initial segments, respectively, of one partial unary algebra. To this purpose we will start with a characterization of pairs of lattices that are weak and strong subalgebra lattices of one partial unary algebra, respectively. Next, we will describe the initial segment lattice of a partial unary algebra. Applying this result, pairs of lattices of strong subalgebras and initial segments will be characterized. Further, we will characterize pairs of lattices of relative and strong subalgebras and also other pairs of subalgebra lattices of one partial unary algebra.

In the paper, new Ramanujan type trigonometric formulae for arguments 2 π/7 and 2 π/9 are presented.

Let k be a field and f : k n → k n be a polynomial isomorphism. We give a formula for f −1 . In particular we show how to solve the equation f = 0.

In the present paper we study generalized left derivations on Lie ideals of rings with involution. Some of our results extend other ones proven previously just for the action of generalized left derivations on the whole ring. Furthermore, we prove that every generalized Jordan left derivation on a 2-torsion free *-prime ring with involution is a generalized left derivation.

Cardinal invariants connected with sums, products and quotients of real functions concerning the family of closed graph functions and the complement in ℝ ℝ of this family are investigate.

The paper is concerned with sup-measurability of a multifunction F defined on the product X × Y of metric spaces with some differentiation bases. We introduce the lower D α property and the upper D α property of multifunction, where α ∈ (0, 1) ⊂ ℝ, and we prove sup-measurabilty of F when it has the upper D α property at ( x, y ), and F ( x , ·) has the lower D α property at y for every ( x, y ) ∈ X × Y . Some application of this theorem to the existence of solutions of differential inclusions f ′ ( x ) ∈ F ( x, f ( x )) is given.

In this present investigation, authors introduce certain subclasses of starlike and convex functions of complex order b , using a linear multiplier differential operator Dλ,μmf(z)$D_{\lambda ,\mu }^m f(z)$. In this paper, for these classes the Fekete–Szegö problem is completely solved. Various new special cases of our results are also pointed out.

We study the problem of exponential decaying for solutions of porous-thermoelasticity system, when time t → ∞. For sufficiently small values of the parameter of intensity of elasticity-porosity interactions the exponential decaying is established. In the considerations we apply the idea of compact decoupling for the system of equations. The exponential decaying property is proved first for the corresponding decoupled system, which is simpler to handle, then the property is derived for the original system.

We present a new class of numerical methods for quasilinear parabolic functional differential equations with initial boundary conditions of the Robin type. The numerical methods are difference schemes which are implicit with respect to time variable. We give a complete convergence analysis for the methods and we show that the new methods are considerable better than the explicit schemes. The proof of the stability is based on a comparison technique with nonlinear estimates of the Perron type for given functions with respect to functional variables. Results obtained in the paper can be applied to differential equations with deviated variables and to differential integral problems.

The concepts of I -convergence and I -Cauchy condition are a generalization of statistical convergence and statistical Cauchy conditions and are dependent on the notion of the ideal I of subsets of the set ℕ of positive integers. In this paper, we shall introduce two new notions of I -uniform continuity and I -uniform boundedness of a function with values in ℝ or in a metric space and then study their basic properties.

The paper contains an existence theorem for local solutions of an initial value problem for a nonlinear integro-differential equation in Banach spaces. The assumptions and proofs are expressed in terms of measures of noncompactness.

In this paper, we introduce the concept of compatible maps and weakly compatible maps of type ( A ) in G -metric spaces.

We study the geometric structures of parabolic geometries. A parabolic geometry is defined by a parabolic subgroup of a simple Lie group corresponding to a subset of the positive simple roots. We say that a parabolic geometry is fundamental if it is defined by a subset corresponding to a single simple root. In this paper we will be mainly concerned with such fundamental parabolic geometries. Fundamental geometries for the Lie algebra of A n type are Grassmann structures. For B n , C n , D n types, we investigate the geometric feature of the fundamental geometries modeled after the quotients of the real simple groups of split type by the parabolic subgroups. We name such geometries Lie tensor product structures. Especially, we call Lie tensor metric structure for B n or D n type and Lie tensor symplectic structure for C n type. For each manifold with a Lie tensor product structure, we give a unique normal Cartan connection by the method due to Tanaka. Invariants of the structure are the curvatures of the connection.

We introduce and study weakly μ -compact μ -space, i.e. μ -space ( X, μ ) in which every cover of X by μ -open sets has a finite subfamily the union of the μ -closures of whose members covers X .

Let X = ( X , +) be an arbitrary topological group. The aim of the paper is to prove a regularity theorem for set-valued subquadratic functions, that is solutions of the inclusion F(s+t)+F(s−t)⊂2F(s)+2F(t),       s,t∈X,$$F(s + t) + F(s - t) \subset 2F(s) + 2F(t),\,\,\,\,\,\,\,s,t \in X,$$ with values in a topological vector space.

In this paper, closedness of certain classes of functions in Y X in the topology of uniform convergence is observed. In particular, we show that the function spaces SC ( X, Y ) of quasi continuous (≡semi-continuous) functions, C α ( X , Y ) of α -continuous functions and L ( X, Y ) of cl-supercontinuous functions are closed in Y X in the topology of uniform convergence.

The aim of this paper is to introduce and characterize the concepts of preopen sets and their related notions in biminimal spaces.

In this paper, a new kind of sets called regular μ -generalized closed (briefly rμg -closed) sets are introduced and studied in a topological space. Some of their properties are investigated. Finally, some characterizations of almost μ -regular, almost μ -normal and mildly μ -normal spaces have been given.

Differential completions and compactifications of differential spaces are introduced and investigated. The existence of the maximal differential completion and the maximal differential compactification is proved. A sufficient condition for the existence of a complete uniform differential structure on a given differential space is given.