GENERAL MATHEMATICS NOTES

Vol. 9, No. 1, March 2012

Contents

Title: C¹-Stable Ergodic Shadowable Invariant Sets and Hyperbolicity

Authors: A. Barzanouni and B. Honary

Abstract: Let f be a diffeomorphism of a closed C^∞ manifold. We define the notion of   C¹stable ergodic shadowing property for a closed f- invariant set Λ and prove that Λ has C¹-stable ergodic shadowing property if and only if it is a hyperbolic elementary set.

PP. 1-6

Title: Boehmians and Elzaki Transform

Author:  S.K.Q. Al-Omari

Abstract: A motivation of the classical Sumudu transform “Elzaki transform” was presented as a closely related transform to the Laplace transform. In the present work, we extend the cited transform to a Schwartz space of distributions of compact support and retain its classical properties. The Elzaki transform is extended to the context of Boehmian spaces and, further, shown to be well defined and linear mapping in the banach space of Lebesgue integrable Boehmians. Certain theorem is also proved in some detail.

PP. 7-15

Title: Coefficient Inequality for Functions Whose Derivative has a Positive Real Part

Authors:  Oladipo A.T. and Fadipe-Joseph O.A.

Abstract: Recently, Acu and Owa [1] further studied the work of Kanas and Ronning [2] by investigating the classes of close - to - convex and α- convex functions normalised with f(w) = f^/(w)-1 = 0 and w is a fixed point in E.  Ghanim and Darus introduced another subclass using the fixed point. Necessary and sufficient conditions were provided for this class. The aim of this paper is to continue the investigation by extending this class of functions to the class S_n(α) defined by the Salagean [4], our result extends some existing ones and new ones are derived.

PP. 16-20

Title: Numerical Solutions of Monic Chebyshev Polynomial on Large Scale Differentiation

Authors: M. El-Kady and N. El-Sawy

Abstract: In this paper, a new formula of the spectral differentiation matrices is presented. Therefore, the numerical solutions for higher-order differential equations are presented by expanding the unknown solution in terms of monic Chebyshev polynomials. The resulting systems of linear equations are solved directly for the values of the solution at the extreme points of the Chebyshev polynomial of order N. The round-off errors during the calculations of differentiation matrices elements are studied. A number of numerical examples are provided in order to show the advantages of the suggested differentiation matrices through comparisons with other works.

PP. 21-37

Title: Connectivity in a Fuzzy Graph and its Complement

Authors: K.R. Sandeep Narayan and M.S. Sunitha

Abstract: Connectivity has important role in the area of applications of fuzzy graphs such as fuzzy neural networks and clustering. In this paper criterion for connectivity of a fuzzy graph and its complement is analysed. The structure of the complement of a fuzzy cycle is also discussed.

PP. 38-43

Title: Lacunary Strongly Almost Generalized Convergence with Respect to Orlicz Function

Author: Ayhan Esi

Abstract: Kizmaz [5] defined the concept of difference sequence spaces. Later some authors introduced and studied some generalizations of this idea. In this paper, we study some properties of [ĉ, M]^θ(Δ^m) -convergence which was defined by Esi [1].

PP. 44-51