GENERAL MATHEMATICS NOTES

Vol. 9, No. 2, April 2012

Contents

Title: Contra-e-Continuous Functions

Authors: M.K. Ghosh and C.K. Basu

Abstract: In 2008, E. Ekici [13] introduced a new class of generalized open sets in a topological space called e-open sets. M. Ozkoc and G Aslim [26], in their recent paper (Bull. Korean Math. Soc. 47 (2010), No. 5, pp. 1025–1036), initiated two strong forms of e-open sets for the study of strongly-θ-e-continuous functions. J. Dontchev [8] introduced the notion of contra continuous functions. In this paper, by means of e-open sets, we introduce and investigate certain ramifications of contra continuous and allied functions, namely, contra-e-continuous, almost-e-continuous, almost weakly-e-continuous and almost contra-e-continuous functions along with their several properties, characterizations and mutual relationships. Further, we introduce new types of graphs, called e-closed, contra-e-closed and strongly contra-e-closed graphs via e-open sets. Several characterizations and properties of such notions are investigated.

PP. 1-18

Title: Absolute Banach Summability of a Factored Conjugate Series

Authors:  S.K. Paikray, U.K. Misra and N.C. Sahoo

Abstract: A theorem for a factored conjugate series is proved in absolute Banach Summability.

PP. 19-31

Title: Determinant and Permanent of Hessenberg Matrix and Fibonacci Type Numbers

Authors: Kenan Kaygisiz and Adem Şahin

Abstract: In this paper, we obtain determinants and permanents of some Hessenberg matrices that give the terms of k sequences of generalized order-k Fibonacci numbers for k=2. These results are important, since k sequences of generalized order-k Fibonacci numbers for k=2 are general form of ordinary Fibonacci sequence, Pell sequence and Jacobsthal sequence.

PP. 32-41

Title: On the Behavior of Numerical solutions with natural of Stability and Controllability of viral dynamical models

Authors: A.A. Elbab, K.M. Hemida and M. Elsaid

Abstract: The system of differential equationsfor simple mathematical models of Human Immune-deficiency Virus (HIV)for the model which components are plasma densities of uninfectedCD4+T helper cells, infectedCD4+Thelper cells and free virus (HIV-1) will be study within the nature of equilibrium points and discuss stability for each of them. After that we study controllability using therapy that uses constant drug dosage of reverse transcription inhibitor (RTI) and protease inhibitor (PI) to help HIV– infected patient to achieve long term non-progressor (LTNP) status. Also, observability and output controllability will apply on this model where in general the state controllability is neither necessary nor sufficient for controlling the output. The analytical treatments are complemented with the numerical solution of the system.

PP. 42-55

Title: Differential Subordinations for New Subclass of Multivalent Functions Defined by Generalized Derivative Operator

Author: Ahmed Sallal Joudah

Abstract: In this paper, we introduce new subclass of multivalent functions by making use of the principle of subordination between these functions and generalized derivative operator. We study several properties like, coefficient estimates, distortion theorem, partial sums and integral means inequalities.

PP. 56-68