Issue 3, Volume 37, September 2012

2012 · Open access

1. A SOLUTION TO AN OPEN PROBLEM ON MATHIEU SERIES POSED BY HOORFAR AND QI GERGŐ NEMES PDF

   ▸ Abstract

   In this paper, the author gives a solution to an open problem about the famous Mathieu series and so obtains a sharp double inequality for bounding the Mathieu series.

   301-310
2. STABILITY AND UNIFORM BOUNDEDNESS RESULTS FOR NON-AUTONOMOUS LIENARD-TYPE EQUATIONS WITH A VARIABLE DEVIATING ARGUMENT CEMIL TUNÇ PDF

   ▸ Abstract

   In this paper, we establish two new results related to the stability and uniform boundedness of the following non-autonomous Liénard type equation with a variable deviating argument $r(t)$: \begin{eqnarray*} &&x^{\prime\prime}(t) + f(t, x(t), x(t − r(t)), x^\prime (t), x^\prime (t − r(t)))x^\prime (t) + g_1(x(t)) \\&&+g_2(x(t − r(t))) = p(t, x(t), x(t − r(t)), x^\prime (t), x^\prime (t − r(t))),\end{eqnarray*} when $p(.) \equiv 0$, and $p(.) \not = 0$, respectively. By the Lyapunov functional approach, we prove our results and give an example to illustrate the theoretical analysis in this work. By this work, we extend and improve an important result in the literature.

   311-325
3. FURTHER RESULTS ON CONVEX FUNCTIONS AND SEPARABLE SEQUENCES WITH APPLICATIONS M. ADIL KHAN, M. NIEZGODA, J. PEČARIĆ PDF

   ▸ Abstract

   In this paper, generalizations are given for some recent results of Niezgoda [M. Niezgoda, Remarks on convex functions and separable sequences, Discrete Math. 308 (2008) 1765-1773]. As applications, two mean value theorems are derived. Gram type inequality is proved. Exponential convexity for differences of power means is shown. Monotonicity of Cauchy type means is shown.

   327-339
4. STRONG CONVERGENCE OF NOOR ITERATION FOR GENERALIZED ASYMPTOTICALLY QUASI-NONEXPANSIVE MAPPINGS IN CAT(0) SPACES G. S. SALUJA PDF

   ▸ Abstract

   In this paper, we establish strong convergence theorems of the Noor iteration for generalized asymptotically quasi-nonexpansive mappings in CAT(0) spaces. Our results improve and extend the corresponding results from the current literature.

   341-355
5. ATTRACTORS FOR NON-AUTONOMOUS SEMILINEAR PARABOLIC EQUATIONS WITH DELAYS CUNG THE ANH, LE VAN HIEU PDF

   ▸ Abstract

   We study the asymptotic behavior of solutions to a class of retarded non-autonomous semilinear parabolic equations with nonlinearities of polynomial type, general delays and time-dependent external forces. The existence of weak solutions for the equations is proved by using the Galerkin method. We then prove the existence of a pullback attractor without restriction on the growth order of polynomial type nonlinearity and on exponential growth of the external force. When the time-dependent external force is a translation bounded function, the existence of a uniform attractor is proved. Finally, we give a relationship between the pullback attractor and the uniform attractor.

   357-377
6. A MODIFIED CLASSICAL ALGORITHM ALPT4C FOR SOLVING A CAPACITATED FOUR-INDEX TRANSPORTATION PROBLEM AAID DJAMEL, NOUI AMEL, LE THI HOAI AN, ZIDNA AHMED PDF

   ▸ Abstract

   In this paper, we focus on the theoretical study and numerical solution of a capacitated four-index transportation problem. This model is not properly treated before, it is linked to significant practical problems, some theoretical properties have been shown. We constructed an algorithm for solving the problem, the implementation of the algorithm with its description has led to an encouraging finding for the digital outcome. On the other hand, the initialization method we used avoids unnecessary assignment and the detective method addresses adequately the problems of degeneracy by making the algorithm robust.

   379-390
7. SOME MULTIPLIER DOUBLE SEQUENCE SPACE KULDIP RAJ, SUNIL K. SHARMA PDF

   ▸ Abstract

   In the present paper we define multiplier double sequence spaces $\chi_M^2[\hat{c},\Delta^m,u,p,q]$ and $\Lambda_M^2[\hat{c},\Delta^m,u,p,q]$ by using a sequence of Orlicz functions $M = (M_{mn})$ and a multiplier function $u = (u_{mn})$. We also make an effort to study some topological properties and inclusion relations between these spaces.

   391-405
8. ON STABILITY OF PROPERTIES OF GENERAL RELATIONAL SYSTEMS UNDER POWERS NITIMA CHAISANSUK, SORASAK LEERATANAVALEE PDF

   ▸ Abstract

   In the paper, we study powers of general relational systems. We solve the problem of finding sufficient conditions under which some properties of relational systems are preserved by powers of these systems. The properties considered are defined with respect to a decomposition of the corresponding index set and they are a common generalization of certain properties of binary and ternary relational systems. We also associate new relational systems with given ones and then study their powers.

   407-418
9. ON THE FIXED-POINT SET AND COMMUTATOR SUBGROUP OF AN AUTOMORPHISM OF A SOLUBLE GROUP B. A. F. WEHRFRITZ PDF

   ▸ Abstract

   Let $\Phi$ be an automorphism of finite order of a group $G$. We deduce consequences for the commutator subgroup $[G, \Phi]$ of $\Phi$ on $G$ of hypotheses such as finiteness and local finiteness on the fixed-point set $C_G(\Phi)$ of $\Phi$ on $G$. We require various solubility or finiteness conditions on $G$ or at least on $[G, \Phi]$.

   419-426
10. INTEGRAL TRANSFORMS RELATED TO THE FOURIER COSINE CONVOLUTION WITH A WEIGHT FUNCTION NGUYEN THANH HONG, NGUYEN MINH KHOA PDF

    ▸ Abstract

    We study a new class of integral transforms from $L_p(\mathbb R_+)$ to $L_q(\mathbb R_+)$, $1 \leq p \leq 2$, $p^{−1} + q^{−1} = 1$, related to the Fourier cosine convolution with a weight function. We obtain necessary and sufficient conditions under which the new transforms are unitary in $L_2(\mathbb R_+)$. A Plancherel type theorem and the boundedness of these integral operators are obtained. We also give several examples of the new transforms kernels.

    427-440