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ISSN : 1226-0657
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Vol.16 No.2
Abstract
In this paper, we obtain the generalized Hyers-Ulam stability of a Cauchy-Jensen functional equation f(x+y, z)-f(x, z)-f(y, z)=0, <TEX>$$2f\;x,\;{\frac{y+z}{2}}-f(x,\;y)-f(x,\;z)=0$$</TEX> in the spirit of P. <TEX>$G{\breve{a}}vruta$</TEX>.
Abstract
Generalizing the approximately convex function which is introduced by D.H. Hyers and S.M. Ulam we establish an approximately convex Schwartz distribution and prove that every approximately convex Schwartz distribution is an approximately convex function.
Abstract
In this paper, we introduce the notions of <TEX>$s{\gamma}$</TEX>-generalized closed sets and <TEX>$s{\gamma}$</TEX>-generalized sets, and investigate some properties for such notions.
Abstract
In the previous work [5] we have determined the group <TEX>${{\varepsilon}_{\sharp}}^{dim+r}^{dim+r}(X)$</TEX> for <TEX>$X\;=\;M(Z_q,\;n+1){\vee}M(Z_q,\;n)$</TEX> for all integers q > 1. In this paper, we investigate the group <TEX>${{\varepsilon}_{\sharp}}^{dim+r}(X)$</TEX> for <TEX>$X\;=\;M(Z{\oplus}Z_q,\;n+1){\vee}M(Z{\oplus}Z_q,\;n)$</TEX> for all odd numbers q > 1.
Abstract
We investigate the multiplicity of the nontrivial periodic solutions for a class of the system of the nonlinear suspension bridge equations with Dirichlet boundary condition and periodic condition. We show that the system has at least two nontrivial periodic solutions by the abstract version of the critical point theory on the manifold with boundary. We investigate the geometry of the sublevel sets of the corresponding functional of the system and the topology of the sublevel sets. Since the functional is strongly indefinite, we use the notion of the suitable version of the Palais-Smale condition.
Abstract
This paper deals with the existence of positive solutions for a kind of multi-point nonlinear fractional differential boundary value problem at resonance. Our main approach is different from the ones existed and our main ingredient is the Leggett-Williams norm-type theorem for coincidences due to O'Regan and Zima. The most interesting point is the acquisition of positive solutions for fractional differential boundary value problem at resonance. And an example is constructed to show that our result here is valid.
Abstract
Let A be a Banach algebra. Suppose there exists a continuous linear Jordan derivation D : A <TEX>$\rightarrow$</TEX> A such that <TEX>$[D(x),\;x]D(x)^2[D(x),\;x]\;{\in}\;rad(A)$</TEX> for all <TEX>$x\;{\in}\;A$</TEX>. Then we have D(A) <TEX>$\subseteq$</TEX> rad(A).
Abstract
The main purpose of this paper is to use the methods of Lattice Dynamical System to establish a global model, which extends the Walrasian evolutionary cobweb model in an independent single local market to the global market evolution over an infinite chain of many local markets interacting each other through a diffusion of prices between them. For brevity of the model, we assume linear decreasing demands and quadratic supplies with naive predictors, and investigate the spatially homogeneous global price dynamics and show that the dynamics is topologically conjugate to that of well-known logistic map and hence undergoes a period-doubling bifurcation route to chaos as a parameter varies through a critical value.