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Vol.16 No.4
Abstract
In this paper, we deal with the following system of nonlinear singular boundary value problems(BVPs) on time scale <TEX>$\mathbb{T}$</TEX> <TEX>$$\{{{{{{x^{\bigtriangleup\bigtriangleup}(t)+f(t,\;y(t))=0,\;t{\in}(a,\;b)_{\mathbb{T}},}\atop{y^{\bigtriangleup\bigtriangleup}(t)+g(t,\;x(t))=0,\;t{\in}(a,\;b)_{\mathbb{T}},}}\atop{\alpha_1x(a)-\beta_1x^{\bigtriangleup}(a)=\gamma_1x(\sigma(b))+\delta_1x^{\bigtriangleup}(\sigma(b))=0,}}\atop{\alpha_2y(a)-\beta_2y^{\bigtriangleup}(a)=\gamma_2y(\sigma(b))+\delta_2y^{\bigtriangleup}(\sigma(b))=0,}}$$</TEX> where <TEX>$\alpha_i$</TEX>, <TEX>$\beta_i$</TEX>, <TEX>$\gamma_i\;{\geq}\;0$</TEX> and <TEX>$\rho_i=\alpha_i\gamma_i(\sigma(b)-a)+\alpha_i\delta_i+\gamma_i\beta_i$</TEX> > 0(i = 1, 2), f(t, y) may be singular at t = a, y = 0, and g(t, x) may be singular at t = a. The arguments are based upon a fixed-point theorem for mappings that are decreasing with respect to a cone. We also obtain the analogous existence results for the related nonlinear systems <TEX>$x^{\bigtriangledown\bigtriangledown}(t)$</TEX> + f(t, y(t)) = 0, <TEX>$y^{\bigtriangledown\bigtriangledown}(t)$</TEX> + g(t, x(t)) = 0, <TEX>$x^{\bigtriangleup\bigtriangledown}(t)$</TEX> + f(t, y(t)) = 0, <TEX>$y^{\bigtriangleup\bigtriangledown}(t)$</TEX> + g(t, x(t)) = 0, and <TEX>$x^{\bigtriangledown\bigtriangleup}(t)$</TEX> + f(t, y(t)) = 0, <TEX>$y^{\bigtriangledown\bigtriangleup}(t)$</TEX> + g(t, x(t)) = 0 satisfying similar boundary conditions.
Abstract
We prove a related fixed point theorem for two pairs of mappings on two intuitionistic fuzzy metric spaces. Our result is maiden in this line.
Abstract
The graph of the parallelogram law is well known, which gives rise to the characterization of an inner product space among normed linear spaces [6]. In this paper we will sketch graphs of its deformations according to our previous paper [7, Theorem 3.1 and 3.2]; each one of which characterizes an inner product space among normed linear spaces. Consequently, the graphs of some classical characterizations of an inner product space follow easily.
Abstract
In this paper we establish various relationships among the generalized integral transform, the generalized convolution product and the first variation for functionals in a Banach algebra S(<TEX>$L_{a,b}^2$</TEX>[0, T]) introduced by Chang and Skoug in [14]. We then derive an inverse integral transform and obtain several relationships involving inverse integral transforms.
Abstract
The notions of P-I-open (closed) mappings, P-I-continuous mappings, P-I-neighborhoods, P-I-irresolute mappings and I-irresolute mappings are introduced. Relations between P-I-open (closed) mappings and I-open (closed) mappings are given. Characterizations of P-I-open (closed) mappings are provided. Relations between a P-I-continuous mapping and an I-continuous mapping are discussed, and characterizations of a P-I-continuous mapping are considered. Conditions for a mapping to be an I-irresolute mapping (resp. P-I-irresolute mapping) are provided.
Abstract
In this study we are concerned with the problem of approximating a locally unique solution of an equation in a Banach space setting using Newton's and modified Newton's methods. We provide weaker convergence conditions for both methods than before [5]-[7]. Then, we combine Newton's with the modified Newton's method to approximate locally unique solutions of operator equations. Finer error estimates, a larger convergence domain, and a more precise information on the location of the solution are obtained under the same or weaker hypotheses than before [5]-[7]. The results obtained here improve our earlier ones reported in [4]. Numerical examples are also provided.
Abstract
In this paper we show that spheres in <TEX>$E^3{\subset}L^n$</TEX> and pseudohyperbolic spaces in <TEX>$L^3{\subset}L^n$</TEX> are the only totally umbilic spacelike surfaces of type (I) in <TEX>$L^n$</TEX>.
Abstract
The method of Lattice Dynamical System is used to establish a global model on an infinite chain of many local markets interacting each other through a diffusion of prices between them. This global model extends the Walrasian evolutionary cobweb model in an independent single local market to the global market evolution. We assume that each local market has linear decreasing demands and quadratic supplies with naive predictors, and investigate the stationary behaviors of global price dynamics and show that their dynamics are conjugate to those of <TEX>$H{\acute{e}}non$</TEX> maps and hence can exhibit complicated behaviors such as period-doubling bifurcations, chaos, and homoclic orbits etc.