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Vol.17 No.1
Abstract
Wu and Zhao [17] provided a semilocal convergence analysis for a Newton-type method on a Banach space setting following the ideas of Frontini and Sormani [9]-[11]. In this study first: we point out inconsistencies between the hypotheses of Theorem 1 and the two examples given in [17], and then, we provide the proof in affine invariant form for this result. Then, we also establish new convergence results with the following advantages over the ones in [17]: weaker hypotheses, and finer error estimates on the distances involved. A numerical example is also provided to show that our results apply in cases other fail [17].
Abstract
We study the geometry of half light like submanifold M of a semi-Riemannian space form <TEX>$\bar{M}$</TEX>(c) subject to the conditions : (a) the screen distribution on M is totally umbilic in M and the coscreen distribution on M is conformal Killing on <TEX>$\bar{M}$</TEX> or (b) the screen distribution is totally geodesic in M and M is irrotational.
Abstract
This paper deals with the second-order differential equation (p(t)x'(t))' + g(t)f(t, x(t), x'(t)) = 0, a.e. in (0, <TEX>$\infty$</TEX>) with the boundary conditions <TEX>$$x(0)={\int}^{\infty}_0g(s)x(s)ds,\;{lim}\limits_{t{\rightarrow}{\infty}}p(t)x'(t)=0,$$</TEX> where <TEX>$g\;{\in}\;L^1[0,{\infty})$</TEX> with g(t) > 0 on [0, <TEX>$\infty$</TEX>) and <TEX>${\int}^{\infty}_0g(s)ds\;=\;1$</TEX>, f is a g-Carath<TEX>$\acute{e}$</TEX>odory function. By applying the coincidence degree theory, the existence of at least one solution is obtained.
Abstract
In this paper, we prove two characterization theorems for real half lightlike submanifold (M,g,S(TM)) of an indefinite Kaehler manifold <TEX>$\bar{M}$</TEX> or an indefinite complex space form <TEX>$\bar{M}$</TEX>(c) subject to the conditions : (a) M is totally umbilical in <TEX>$\bar{M}$</TEX>, or (b) its screen distribution S(TM) is totally umbilical in M.
Abstract
In [17, 18], the fuzzy stability problems for the Cauchy additive functional equation and the Jensen additive functional equation in fuzzy Banach spaces have been investigated. In this paper, we prove the generalized Hyers-Ulam stability of the following quadratic functional equations in fuzzy Banach spaces: (0.1) f(x + y) + f(x - y) = 2f(x) + 2f(y), (0.2) f(ax + by) + f(ax - by) = <TEX>$2a^2 f(x)\;+\;2b^2f(y)$</TEX> for nonzero real numbers a, b with <TEX>$a\;{\neq}\;{\pm}1$</TEX>.
Abstract
This paper gives some sorts of weakly cancellative of elements which are to be or not to be left magnifying elements in certain semigroups and gives a semilattice congruence in a weakly separative semigroup.
Abstract
Let R be a 2-torsion free <TEX>$\sigma$</TEX>-prime ring with an involution <TEX>$\sigma$</TEX>, U a nonzero square closed <TEX>$\sigma$</TEX>-Lie ideal, Z(R) the center of Rand d a derivation of R. In this paper, it is proved that d = 0 or <TEX>$U\;{\subseteq}\;Z(R)$</TEX> if one of the following conditions holds: (1) <TEX>$d(xy)\;-\;xy\;{\in}\;Z(R)$</TEX> or <TEX>$d(xy)\;-\;yx\;{\in}Z(R)$</TEX> for all x, <TEX>$y\;{\in}\;U$</TEX>. (2) <TEX>$d(x)\;{\circ}\;d(y)\;=\;0$</TEX> or <TEX>$d(x)\;{\circ}\;d(y)\;=\;x\;{\circ}\;y$</TEX> for all x, <TEX>$y\;{\in}\;U$</TEX> and d commutes with <TEX>$\sigma$</TEX>.
Abstract
We employ the methods of Lattice Dynamical System to establish a global model extending the Walrasian evolutionary cobweb model in an independent single local market to the global market evolution over an infinite chain of many local markets with interaction of each other through a diffusion of prices between them. For brevity of the model, we assume linear decreasing demands and logistic supplies with naive predictors, and investigate the traveling wave behaviors of global price dynamics and show that their dynamics are conjugate to those of H<TEX>$\acute{e}$</TEX>non maps and hence can exhibit complicated behaviors such as period-doubling bifurcations, chaos, and homoclic orbits etc.
Abstract
In this paper, we study the root system of rank 2 symmetric hyperbolic Kac-Moody algebras. We give the sufficient conditions for existence of imaginary roots of square length -2k (<TEX>$k\;{\in}\;\mathbb{Z}$</TEX>>0). We also give several relations between the roots on g(A).