GENERAL MATHEMATICS NOTES

Vol. 7, No. 1, November 2011 

Contents

 Title: On Some Properties of I₂-Convergence and I₂-Cauchy of Double Sequences

 Authors: Erdinç Dündar and Bilal Altay

 Abstract: In this paper we study the concepts of I-Cauchy, I*-Cauchy sequences for double sequence in a linear metric space and also we investigate I-convergent, I*-convergence for double sequences of functions in a linear metric space and then we show the relation between them.

PP. 1-12

 Title: On Totally sg-Continuity, Strongly sg-Continuity and Contra sg-Continuity

 Authors: O. Ravi, S. Ganesan and S. Chandrasekar

Abstract: In this paper, sg-closed sets and sg-open sets are used to define and investigate a new class of functions. Relationships between this new class and other classes of functions are established.

PP. 13-24

Title: Some Higher-Order Families of Methods for Finding Simple Roots of Nonlinear Equations

 Authors: Jafar Biazar and Behzad Ghanbari

Abstract: In this paper, a new fifth-order family of methods free from second derivative is obtained. This new iterative family contains the King’s family, which is one of the most well-known family of methods for solving nonlinear equations, and some other known methods as its particular case. To illustrate the efficiency and performance of proposed family, several numerical examples are presented. Numerical results illustrate better efficiency and performance of the presented methods in comparison with the other compared fifth-order methods. Due to that, they can be effectively used for solving nonlinear equations.

PP. 25-32

Title: Application of Fractional Calculus Operators to Related Areas

Author: Kishan Sharma

Abstract: In this paper a new function called as extended K-function, which is an extension of the generalization of the Mittag-Leffler function [10,11] and its generalized form introduced by Prabhakar [20], is introduced and studied by the author in terms of some special functions and  derived the relations that exists between the extended K-function and the operators of Riemann-Liouville fractional integrals and derivatives.

PP. 33-40

Title: Alternating Direction Implicit Formulation of the Differential Quadrature Method for Solving the Unsteady State Two-Dimensional Convection-Diffusion Equation

 Authors: A.S.J. Al-Saif  and Mohammed J. Al-Kanani

Abstract: In this paper, we propose alternating direction implicit formulation of the differential quadrature method (ADI-DQM) for calculating the numerical solutions of the two-dimensional unsteady state convection-diffusion equation with appropriate initial and boundary conditions. The results confirm that this method has a high accuracy, good convergence and less workload compared with the other numerical methods. 

PP. 41-50

 Title: Frames and Matrix Representation of Operators

 Authors: Shiv Kumar and Balbir Singh

 Abstract: In this paper we obtained analogous results of Duffin and Schaeffer [8] by using a matrix representation of operators on a Hilbert space with Bessel sequences, frames and Riesz bases.

PP. 51-58

Title: Application of Approximate Best Proximity Pairs

 Authors: S. A. M. Mohsenalhosseini, H. Mazaheri, M. A. Dehghan and M. Bagheshahi

 Abstract: In this paper we give ky fans approximate best proximity theorem and Picard-Lindeloffs approximate best proximity theorem, then illustrate a few applications where we derive results in fixed point theory, approximation theory, boundary value problems theorem.

PP. 59-65