Caspian Journal of Mathematical Sciences
Volume:3 Issue: 1, Winter Spring 2014

We study the existence of periodic solutions of the totally nonlinear neutral difference equation with variable delay 4x (t) = −a (t) x 3 (t + 1) + c (t) 4x (t − g (t)) + G t, x3 (t), x3 (t − g (t))
, ∀t ∈ Z. We invert the given equation to construct a fixed point mapping expressed as a sum of a large contraction and a compact map. We show that such a sum of mappings fits very nicely into the framework of Krasnoselskii-Burton’s fixed point theorem so that the existence of periodic solutions is readily concluded. The obtained results extend the work of Ardjouni and Djoudi [1]. Keywords: Fixed point, Large contraction, Periodic solutions, Totally nonlinear neutral differential equations

In this paper, we study B-focal curves of biharmonic B -general helices according to Bishop frame in the Heisenberg group Heis   Finally, we characterize the B-focal curves of biharmonic B- general helices in terms of Bishop frame in the Heisenberg group Heis

In this study a numerical method is developed to solve the Hammerstein integral equations. To this end the kernel has been approximated using the leastsquares approximation schemes based on Legender-Bernstein basis. The Legender polynomials are orthogonal and these properties improve the accuracy of the approximations. Also the nonlinear unknown function has been approximated by using the Bernstein basis. The useful properties of Bernstein polynomials help us to transform Hammerstein integral equation to solve a system of nonlinear algebraic equations.

In this paper, we establish an existence result of the solution for an generalized strong vector variational inequality already considered in the literature and as applications we obtain a new coincidence point theorem in Hilbert spaces.

‎In this paper we defined the vertex removable cycle in respect of the following‎, ‎if $F$ is a class of graphs(digraphs)‎ ‎satisfying certain property‎, ‎$G in F $‎, ‎the cycle $C$ in $G$ is called vertex removable if $G-V(C)in in F $.‎ ‎The vertex removable cycles of eulerian graphs are studied‎. ‎We also characterize the edge removable cycles of regular‎ ‎graphs(digraphs).‎

We show how Daubechies wavelets are used to solve Kuramoto-Sivashinsky type equations with periodic boundary condition‎. ‎Wavelet bases are used for numerical solution of the Kuramoto-Sivashinsky type equations by Galerkin method‎. ‎The numerical results in comparison with the exact solution prove the efficiency and accuracy of our method‎.

In this paper, we present two new families of third-order and fourth-order methods for finding multiple roots of nonlinear equations. Each of them requires one evaluation of the function and two of its first derivative per iteration. Several numerical examples are given to illustrate the performance of the presented methods.

In this paper, we give a new fixed point theorem forWeakly quasi-contraction maps in metric spaces. Our results extend and improve some fixed point and theorems in literature.

In this work, we give parallel transport frame of a curve and we introduce the relations between the frame and Frenet frame of the curve in 4-dimensional Euclidean space. The relation which is well known in Euclidean 3-space is generalized for the …rst time in 4-dimensional Euclidean space. Then we obtain the condition for spherical curves using the parallel transport frame of them. The condition in terms of { and  is so complicated but in terms of k1 and k2 is simple. So, parallel transport frame is important to make easy some complicated characterizations. Moreover, we characterize curves whose position vectors lie in their nor- mal, rectifying and osculating planes in 4-dimensional Euclidean space E4:

In this paper, we use modified Laplace decomposition method to solving initial value problems (IVP) of the second order ordinary differential equations. Theproposed method can be applied to linear and nonlinearproblems

We call a module M , quasi-catenary if for each pair of quasi-prime submodules K and L of M with K  L all saturated chains of quasi-prime submodules of M from K to L have a common finite length. We show that any homomorphic image of a quasi-catenary module is quasi-catenary. We prove that if M   is a module with following properties: (i) Every quasi-prime submodule of M has finite quasi-height; (ii) For every pair of K  L of quasi-prime submodules ofM, q−height(L/K ) = q− height(L) − q − height(K); then M is quasi-catenary.

‎In this paper‎, ‎we present a new modification of Chebyshev-Halley‎ ‎method‎, ‎free from second derivatives‎, ‎to solve nonlinear equations‎. ‎The convergence analysis shows that our modification is third-order‎ ‎convergent‎. ‎Every iteration of this method requires one function and‎ ‎two first derivative evaluations‎. ‎So‎, ‎its efficiency index is‎ ‎$3^{1/3}=1.442$ that is better than that of Newton method‎. ‎Several‎ ‎numerical examples are given to illustrate the performance of the‎ ‎presented method‎.

Some scientists are interesting to study in area of harvested ecological modelling. The harvested population dynamics is more realistic than other ecological models. In the present paper, some of the Lotka-Volterra predator-prey models have been considered. In the said models, existing species are harvested by constant or variable growth rates. The behavior of their solutions has been analyzed in the stability sense. The employed methods are linearization and Lyapunove function.

Let (X, d) be a compact metric space and let K be a nonempty compact subset of X. Let α ∈ (0, 1] and let Lip(X, K, dα ) denote the Banach algebra of all continuous complex-valued functions f on X for which pα,K(f) = sup{ |f(x)−f(y)| dα(x,y) : x, y ∈ K, x 6= y} < ∞ when equipped the algebra norm ||f||Lip(X,K,dα) = ||f||X + pα,K(f), where ||f||X = sup{|f(x)| : x ∈ X}. We denote by lip(X, K, dα ) the closed subalgebra of Lip(X, K, dα ) consisting of all f ∈ Lip(X, K, dα ) for which |f(x)−f(y)| dα(x,y) → 0 as d(x, y) → 0 with x, y ∈ K. In this paper we obtain a sufficient condition for density of a linear subspace or a subalgebra of Lip(X, K, dα ) in (Lip(X, K, dα ), || · ||Lip(X,K,dα)) (lip(X, K, dα ) in (lip(X, K, dα ), || · ||Lip(X,K,dα)), respectively). In particular, we show that the Lipschitz algebra Lip(X, dα ) is dense in (Lip(X, K, dα ), k · kLip(X,K,dα)) for α ∈ (0, 1] and Lip(X, d) and the little Lipschitz algebra lip(X, dα ) are dense in (lip(X, K, dα ), k · kLip(X,K,dα)) for α ∈ (0, 1).