Issue 1, Volume 37, March 2012

2012 · Open access

1. GENERALIZED GROWTH OF SOLUTIONS TO A CLASS OF ELLIPTIC PARTIAL DIFFERENTIAL EQUATIONS G. S. SRIVASTAVA, SUSHEEL KUMAR PDF

   ▸ Abstract

   In the present paper, we study the generalized growth of solu-tions to a class of elliptic partial differential equations. The characterizations of generalized order and generalized type of solutions to a class of elliptic par-tial differential equations have been obtained in terms of its Taylor’s series coefficients.

   11-21
2. CONVERGENCE THEOREMS FOR PSEUDO-COMPLETE LOCALLY CONVEX ALGEBRAS U. N. BASSEY PDF

   ▸ Abstract

   The set of bounded elements of a locally convex algebra is characterized as the union of certain naturally defined normed subalgebras. Pseudocomplete locally convex algebras are characterized in terms of the completeness of these subalgebras. In this paper it is proved, among other results, that a convergent sequence of elements in a bounded pseudo-complete locally convex strict inductive limit algebra is locally convergent. Along the way, a theorem on $i$-bounded sets is obtained, which identifies non-normable locally convex algebras in which every bounded subset is $i$-bounded.

   23-30
3. PENALTY FUNCTIONS FOR THE VECTOR VARIATIONAL INEQUALITY PROBLEM DAU XUAN LUONG PDF

   ▸ Abstract

   In this paper we apply the penalty function method to the vector variational inequality problem, in order to transform a constrained problem, referred to as the original problem, into a sequence of simpler, unconstrained problems, referred to as the penalized problems. We show that any limit point of a sequence of solutions of the penalized problems is a solution of the original problem. Moreover, under certain assumptions on the feasible region $D$ and the function $\mathbf{F}$, we can show that every penalized problem has a solution, and that a sequence of solutions of the penalized problems always has at least one limit point. As far as we know, this is the first study on solving a vector variational inequality problem using the penalty function method.

   31-40
4. ON THE STRUCTURE OF SOLUTION SETS OF AN INTEGRAL EQUATION IN A FRÉCHET SPACE DO HOAI VU, LE HOAN HOA PDF

   ▸ Abstract

   In this paper we consider Aronszajn’s-type topological charac- terization (or compact $R_{\delta}$ property) of the set of solutions to the following integral equation $$x(t)=V\left(t, x(\theta_1(t)), \int_0^t F\left(t, s, x(\theta_2(s)), \int_0^t r(s, \tau)x(\theta_3(\tau))d\tau\right)\right)+\int_0^t K(t, s)g(s, x(\theta_4(s)))ds,$$ where $t\in [0,\infty);$ $\theta_i: [0,\infty)\to [0,\infty),$ $i=1, 2, 3, 4;$ $K: [0,\infty) \times [0,\infty) \to L(E,E);$ $V: [0,\infty) \times E \times E\to E$; $F: [0,\infty) \times [0,\infty) \times E \times E\to E$; $r: [0,\infty)\times [0,\infty) \to R$; $g: [0,\infty)\times E\to E$; $E$ is a real Banach space with norm $|.|$; $L(E,E)$ the Banach space of continuous linear operators with domain $E$ and range in $E$.

   41-51
5. A NOTE ON WEAKLY $s$-PERMUTABLY EMBEDDED AND WEAKLY $s$-SUPPLEMENTED SUBGROUPS CHANGWEN LI PDF

   ▸ Abstract

   Suppose that $G$ is a finite group and $H$ is a subgroup of $G$. $H$ is called weakly $s$-permutably embedded in $G$ if there are a subnormal subgroup $T$ of $G$ and an $s$-permutably embedded subgroup $H_{se}$ of $G$ contained in $H$ such that $G = HT$ and $H \cap T \le H_{se}$; $H$ is called weakly $s$-supplemented in $G$ if there is a subgroup $T$ of $G$ such that $G = HT$ and $H \cap T \le H_{sG}$, where $H_{sG}$ is the subgroup of $H$ generated by all those subgroups of $H$ which are $s$-permutable in $G$. We investigate the influence of weakly $s$-permutably embedded and weakly $s$-supplemented subgroups on the $p$-nilpotency of finite groups. Some recent results are generalized.

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6. A NOTE ON THE INEQUALITIES FOR A POLYNOMIAL AND ITS DERIVATIVE PRASANNA KUMAR N PDF

   ▸ Abstract

   In this paper, we obtain new bounds concerning the maximum moduli of complex polynomials of lacunary type and their derivatives with restricted zeros. These results generalize and refine upon all the earlier results.

   63-69
7. AN APPLICATION OF ZBAG\v{A}NU CONSTANT IN FIXED POINT THEORY ZHANFEI ZUO PDF

   ▸ Abstract

   Some sufficient conditions for Banach spaces have normal struc- ture were gotten in terms of Zbag\v{a}nu constant, the weak orthogonality coeffi- cient and the weakly convergent sequence coefficient, which imply the existence of fixed points for single valued and multivalued nonexpansive mappings.

   71-77
8. SOME NOTES ON WEAKLY REVERSIBLE RINGS JUNCHAO WEI PDF

   ▸ Abstract

   In this paper, we give some properties of weakly reversible rings, such as weakly reversible rings are left min-abel and directly finite. Next, we show that $R$ is a strongly regular ring if and only if $R$ is a weakly reversible regular ring. Finally, we give some applications: Let $R$ be a weakly reversible ring. Then (1) $R$ is clean if and only if $R$ is exchange; (2) If $R$ is exchange, then $R$ has stable range one; (3) If $R$ is a clean ring, then $R$ is a tb-ring.

   79-87
9. THE RATE OF INCREASE OF MEAN VALUES OF FUNCTIONS IN WEIGHTED HARDY SPACES CHENGJI XIONG, JUNMING LIU PDF

   ▸ Abstract

   Let $0 < p < \infty$ and $0 \le q < \infty$. For each $f$ in the weighted Hardy space $H_{p,q}$, we show that $d\| f_r\| ^p_{p,q}/dr$ grows at most like $o(1/1-r)$ as $r\to 1$.

   89-93
10. A NEW EXTRAGRADIENT ITERATION ALGORITHM FOR BILEVEL VARIATIONAL INEQUALITIES PHAM NGOC ANH PDF

    ▸ Abstract

    In this paper, we introduce an approximation extragradient itera- tion method for solving bilevel variational inequalities involving two variational inequalities and we show that these problems can be solved by projection se- quences and fixed point techniques. We obtain a strong convergence of three iteration sequences generated by this method in a real Hilbert space.

    95-107
11. HERMITE-HADAMARD TYPE INEQUALITIES FOR HIGHER ORDER CONVEX FUNCTIONS AND VARIOUS QUADRATURE RULES IVA FRANJI\'{C}, JOSIP PE\v{C}CARI\'{C} PDF

    ▸ Abstract

    Hermite-Hadamard type inequalities are given for the higher order convex functions and the general three, four and five point quadrature rules, as well as for their corrected counterparts. Specifically, Hermite-Hadamard type estimates are obtained for various classical quadrature rules, such as the Simpson, dual Simpson, Simpson 3/8, Maclaurin, the Gauss 2 and 3-point, the Lobatto 4 and 5-point rule, and their corrected variants.

    109-120
12. ON MEROMORPHIC MAPPINGS IN SEVERAL COMPLEX VARIABLES WITH MAXIMAL DEFICIENCY SUM FOR MOVING TARGETS PHAM DUC THOAN, PHAM VIET DUC PDF

    ▸ Abstract

    In this paper, a theorem on the deficiency of meromorphic map- pings in several complex variables with maximal deficiency sum for moving hyperplane targets is given.

    121-135
13. ON EXISTENCE OF WEAK SOLUTIONS OF NEUMANN PROBLEM FOR A SYSTEM OF SEMILINEAR ELLIPTIC EQUATIONS IN AN UNBOUNDED DOMAIN TRINH THI MINH HANG, HOANG QUOC TOAN PDF

    ▸ Abstract

    The goal of this paper is to study the existence of non-trivial weak solution for the following system of nonlinear elliptic equations: \begin{eqnarray*} &&-\mathrm{div}(h_1(x)\nabla u)+a(x)u=f(x,u,v) \text{ in } \Omega\\ && -\mathrm{div}(h_2(x)\nabla v)+b(x)v=g(x,u,v) \text{ in } \Omega \end{eqnarray*} with Neumann condition: \begin{gather*} \dfrac{\partial u}{\partial n}=0,\quad \dfrac{\partial v}{\partial n}=0\\ u(x)\longrightarrow 0, \quad v(x)\longrightarrow 0 \text{ as } |x|\longrightarrow +\infty \end{gather*} where $\Omega \subset R^N, N \ge 3$ is an unbounded domain with smooth bounded boundary $\partial\Omega$, and $h_i(x)\in L^1_{loc}(\overline{\Omega})$, $i=1,2$, $\overline{\Omega}=\Omega\cup\partial\Omega$. The solutions will be obtained in a subspace of the space $H^1(\Omega)$ and the proofs rely essentially on a variation of the Mountain Pass Theorem in [7].

    137-147
14. BOUNDEDNESS FOR MAXIMAL MULTILINEAR BOCHNER-RIESZ OPERATORS ON CERTAIN HARDY SPACES ZHOU XIAOSHA PDF

    ▸ Abstract

    In this paper, the boundedness for the maximal multilinear Bochner-Riesz operators on certain Hardy and Herz-Hardy spaces are obtained.

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