Band 45, Heft 3

We prove the result announced by the title as well as some of its consequences.

In this paper we characterize finite directly indecomposable monogenic entropic quasigroups with quasi-identity.

In this note, we establish a new inequality of Ostrowski-type for double integrals involving functions of two independent variables by using fairly elementary analysis.

The purpose of the present paper is to derive characterization theorem and radius of starlikeness for certain class of p -valent analytic functions. In connection with these results some more properties are discussed.

In this paper, we give a necessary and sufficient condition for the existence of at least one Ψ-bounded solution of a linear nonhomogeneous Lyapunov matrix differential equation. In addition, we give a result in connection with the asymptotic behavior of the Ψ-bounded solutions of this equation.

In this paper we obtain the existence of solutions and Carathéodory type solutions of the dynamic Cauchy problem in Banach spaces for functions defined on time scales xΔ(t)=f(t,x(t)),x(0)=x0,t∈Ia,$$\matrix{{x^\Delta (t) = f(t,x(t)),} \hfill & {} \hfill \cr {x(0) = x_0 ,} \hfill & {t \in I_a ,} \hfill } $$ where f is continuous or f satisfies Carathéodory conditions and some conditions expressed in terms of measures of noncompactness. The Mönch fixed point theorem is used to prove the main result, which extends these obtained for real valued functions.

Using critical point theory and some monotonicity results we consider the existence and multiplicity of solutions to nonlinear discrete boundary value problems represented as a nonlinear system Au = λ f ( u ) with parameter λ > 0 and with matrix A being not necessarily positive definite. We provide applications for discrete version of the Emden–Fowler equation.

In this paper we define ℓ ∞ ( M, p, ϕ, q, s ), c ( M, p, ϕ, q, s ) and c 0 ( M, p, ϕ, q, s ), the sequence spaces on a seminormed complex linear space, using an Orlicz function. We give various properties and some inclusion relations on this space.

The purpose of this paper is to determine spectrum and fine spectrum of newly introduced operator Δuvw2$\Delta _{uvw}^2 $ on sequence space l 1 . The operator Δuvw2$\Delta _{uvw}^2 $ on sequence space l 1 is defined by Δuvw2x=(unxn+vn-1xn-1+wn-2xn-2)n=0∞$\Delta _{uvw}^2 x = \left( {u_n x_n + v_{n - 1} x_{n - 1} + w_{n - 2} x_{n - 2} } \right)_{n = 0}^\infty $ with x −1 , x −2 = 0, where x = ( x n ) ∈ l 1 , u = ( u k ) is either constant or strictly increasing sequence of positive real numbers with U=limk→∞uk$U = \mathop {\lim }\limits_{k \to \infty } u_k $, v = ( v k ) is a sequence of real numbers such that v k ≠ 0 for each k ∈ ℕ 0 with V=limk→∞vk≠0$V = \mathop {\lim }\limits_{k \to \infty } v_k \ne 0$ and w = ( w k ) is a non-increasing sequence of positive real numbers such that w k ≠ 0 for each k ∈ ℕ 0 with W=limk→∞wk≠0$W = \mathop {\lim }\limits_{k \to \infty } w_k \ne 0$. In this paper we have obtained the results on spectrum and point spectrum for the operator Δuvw2$\Delta _{uvw}^2 $ over sequence space l 1 . We have also obtained the results on continuous spectrum σc(Δuvw2,l1)$\sigma _c \left( {\Delta _{uvw}^2 ,l_1 } \right)$, residual spectrum σr(Δuvw2,l1)$\sigma _r \left( {\Delta _{uvw}^2 ,l_1 } \right)$ and fine spectrum of the operator Δuvw2$\Delta _{uvw}^2 $ on sequence space l 1 .

Using compatibility of type ( N ) and (E-A) property of hybrid pair of mappings we obtain some new coincidence and common fixed point theorems under strict contractive conditions in symmetric (semi-metric) space.

The purpose of this paper is to present some fixed point theorems for certain weakly contractive mappings, known as weakly ( φ − ψ )-contractive mappings, in a complete metric space endowed with a partial ordering. Subsequently, we apply our main results to obtain a solution of a first order periodic problem and study the possibility of optimally controlling the solutions of ordinary differential equations via dynamic programming.

In the paper Gaussian curvature of Bergman metric on the unit disc and the dependence of this curvature on the weight function has been studied.

Consider submanifolds in the nested space. For a compact pseudoumbilical submanifold with parallel mean curvature vector of a Riemannian submanifold with constant curvature immersed in a quasi-constant curvature Riemannian manifold, two sufficient conditions are given to let the pseudo-umbilical submanifold become a totally umbilical submanifold.

This paper deals with the abstract density topologies in the family of Lebesgue measurable sets generated by an operator similar to the density lower operator defined in the family of measurable sets.

Real valued homomorphisms on the algebra of smooth functions on a differential space are described. The concept of generators of this algebra is emphasized in this description.

A new class of functions called ‘quasi cl-supercontinuous functions’ is introduced. Basic properties of quasi cl-supercontinuous functions are studied and their place in the hierarchy of variants of continuity that already exist in the mathematical literature is elaborated. The notion of quasi cl-supercontinuity, in general, is independent of continuity but coincides with cl-supercontinuity (≡ clopen continuity) (Applied General Topology 8(2) (2007), 293–300; Indian J. Pure Appl. Math. 14(6) (1983), 767–772), a significantly strong form of continuity, if range is a regular space. The class of quasi cl-supercontinuous functions properly contains each of the classes of (i) quasi perfectly continuous functions and (ii) almost cl-supercontinuous functions; and is strictly contained in the class of quasi z -supercontinuous functions. Moreover, it is shown that if X is sum connected (e.g. connected or locally connected) and Y is Hausdorff, then the function space L q ( X, Y ) of all quasi cl-supercontinuous functions as well as the function space L δ ( X, Y ) of all almost cl-supercontinuous functions from X to Y is closed in Y X in the topology of pointwise convergence.

In the present paper, we have made a category theoretic and lattice theoretic study of some nearness-like structures in the L -approach theory. Using L -grills, the notion of L -approach grill structure is introduced as a characterization of L -approach grill merotopy on X ; their categorical perspectives and implications are also investigated. A number of illustrative examples are included.

In this paper, introducing a contraction principle on generalized metric spaces, a generalization of Banach’s fixed point theorem is obtained under the completeness condition of the space. Moreover, it is established that, using such contraction principle, completeness of the generalized metric space can be characterized.

We analyse a finite difference scheme for von Foerster–McKendrick type equations with functional dependence forward in time and backward with respect to one dimensional spatial variable. Some properties of solutions of a scheme are given. Convergence of a finite difference scheme is proved. The presented theory is illustrated by a numerical example.