**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

**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

**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

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