In this paper we investigate connections between the class of Cohen strongly summing multilinear operators and other classes of multilinear mappings, such as multiple summing and strongly summing mappings (in the sense of Dimant). As a consequence of our results, we show that if $Y$ is a $\mathcal{L}_{p^{\ast }}$-space and $X_{1},...,X_{m}$ are $\mathcal{L}_{p}$-spaces ($1<p<\infty $ and $1/p+1/p^{\ast }=1)$, then every multiple $p^{\ast }$-summing $m$-linear operator is strongly $p^{\ast }$-summing.

We consider the problem of application of the method of averaging to the asymptotic approximation of solutions of ordinary differential inclusions of the form $\dot x(t) \in f(t/\varepsilon,x(t))$. Our result is formulated in both classical mathematics and nonstandard analysis; its proof uses some methods of nonstandard analysis.

Making use of a fractional derivative operator, we introduce and investigate two new classes $K_{j}(p,\lambda ,b,\beta )$ and $L_{j}(p,\lambda ,b,\beta ,\mu )$ of multivalently analytic functions of complex order. In this paper we obtain the coefficient estimates and inclusion relationships involving the $(j,\delta )-$ neighborhood of various subclasses of multivalently analytic functions of complex order.

In the present paper we introduce generalized Bleimann, Butzer and Hahn operators $F_n(f;p;x)$. The form of the operator discussed, makes results helpful from the computational point of view. Here we have studied the rate of convergence of $F_n(f;p;x)$. The current work extends the similar results of V. Gupta, H. M. Srivastava, A. Lupas, O. Dogru.

We establish that the elliptic equation $\Delta u+f(x,u)+g(|x|)x\cdot \nabla u=0$, where $x\in\mathbb{R}^{n}$, $n\geq3$, and $|x| >A>0$, has a positive solution which decays to $0$ as $|x|\rightarrow +\infty$ under mild restrictions on the functions $f,g$. The main theorem improves substantially upon the conclusions of the recent paper [M. Ehrnström, Positive solutions for second-order nonlinear differential equations, Nonlinear Anal. TMA 64 (2006), 1608--1620]. Its proof relies on a sharp result of non-oscillation of linear ordinary differential equations and on the comparison method.

In this note we study the dynamical behaviour of the uniform limit of a sequence of continuous self-maps on a compact metric space satisfying (topological) transitivity or other related properties. Moreover, some conditions for the transitivity of a limit are given.

We introduce three variants of a symmetric matrix game corresponding to three ways of comparing two partitions of a fixed integer ($\sigma$) into a fixed number ($n$) of parts. In the random variable interpretation of the game, each variant depends on the choice of a copula that binds the marginal uniform cumulative distribution functions (cdf) into the bivariate cdf. The three copulas considered are the product copula $T_{\bf P}$ and the two extreme copulas, i.e. the minimum copula $T_{\bf M}$ and the Łukasiewicz copula $T_{\bf L}$. The associated games are denoted as the $(n,\sigma)_{\bf P}$, $(n,\sigma)_{\bf M}$ and $(n,\sigma)_{\bf L}$ games. In the present paper, we characterize the optimal strategies of the $(n,\sigma)_{\bf M}$ and $(n,\sigma)_{\bf L}$ games and compare them to the optimal strategies of the $(n,\sigma)_{\bf P}$ games. It turns out that the characterization of the optimal strategies is completely different for each game variant.

In this paper we study complete vertical graphs of constant mean curvature in the Hyperbolic and Steady State spaces. We first derive suitable formulas for the Laplacians of the height function and of a support-like function naturally attached to the graph; then, under appropriate restrictions on the values of the mean curvature and the growth of the height function, we obtain necessary conditions for the existence of such a graph. In the two-dimensional case we apply this analytical framework to state and prove Bernstein-type results in each of these ambient spaces.

We consider a connected symplectic manifold $M$ acted on properly and in a Hamiltonian fashion by a connected Lie group $G$. If $G$ is compact, then we characterize the symplectic manifolds whose squared moment map is constant. We also give a sufficient condition for $G$ to admit a symplectic orbit. Then we study the case when $G$ is a non-compact Lie group proving splitting results for symplectic manifolds.

This is a final step in a local classification of pseudo-Riemannian manifolds with parallel Weyl tensor that are not conformally flat or locally symmetric.

Let ${\cal S}$ be a locally compact semigroup and $M_a({\cal S})$ be its semigroup algebra. In this paper, we investigate inner invariant means on $L^\infty({\cal S},M_a({\cal S}))$ of all $M_a( {\cal S})$-measurable complex-valued bounded functions on ${\cal S}$ and its closed subspace $C_b({\cal S})$, the space of all bounded continuous complex-valued functions on ${\cal S}$. We also study topological inner invariant means on certain closed subspaces $X$ of $L^\infty({\cal S},M_a({\cal S}))$ and their relation with inner invariant means on $X$.

In this paper we investigate amenability, and essential amenability of the convolution Banach algebra $A(K)$ for a compact hypergroup $K$ together with their applications to convolution Banach algebras $L^p(K)$ $(1<p\leq\infty)$, and $C(K)$.

Appealing to the familiar convolution structure of analytic functions, we introduce a general class of multivalently analytic functions, and derive several properties and characteristics of this function class by applying the differential subordination techniques. Relevant connections of the results stated here with those obtained in earlier works are also pointed out.

Tompa and Woll constructed a zero-knowledge proof of knowing a square root of $X$ mod $N$, where $N$ is the product of two large, secret primes. In this paper, we construct a zero-knowledge proof of knowing a square root of $X_1$ or $X_2$ mod $N$. Compared with the existing solution to this problem, ours is significantly simpler.

The concept of differential subordination was introduced in [4] by S.S. Miller and P.T. Mocanu and the concept of strong differential subordination was introduced in [1], [2], [3] by J.A. Antonino and S. Romaguera. In [7] we have studied the strong differential subordinations in the general case and in [8] we have studied the first order linear strong differential subordinations. In [6] we have studied the second order linear strong differential subordinations. In this paper we study the second order non-linear strong differential subordinations. Our results may be applied to deduce sufficient conditions for univalence in the unit disc, such as starlikeness, convexity, alpha-convexity, close-to-convexity respectively.

Here, we are going to extend Mycielski's conjecture to higher homotopy groups. Also, for an $(n-1)$-connected locally $(n-1)$-connected compact metric space $X$, we assert that $\pi^{top}_{n}(X)$ is discrete if and only if $\pi_{n}(X)$ is finitely generated. Moreover, $\pi^{top}_{n}(X)$ is not discrete if and only if it has the power of the continuum.