Journal of Mathematical Extension
Volume:11 Issue: 2, Spring 2017

In this paper, it is attempted to approximate the real and complex roots of nonlinear equations. For this reason, by considering the convergence conditions of Adomian decomposition method for solving functional equations, a new appropriate method is presented. It will be shown that the proposed method can be computed suitable approximate real and complex roots of a given function more efficient than Maple software. Furthermore, with providing some examples the aforementioned cases are dealt with numerically.

Hepatitis C is the leading cause of death among individuals infected with human. Here, we present a deterministic model for HCV and HIV infections transmission and use the model to assess the potential impact of antiviral therapy. The model is based on the Susceptible-Infective-Removed-Susceptible (SIRS) compartmental structure with chronic primary infection and possibility of reinfection. Important epidemiologic thresholds such as the basic and control reproduction numbers and a measure of treatment impact are derived. We find that if the control reproduction number is greater than unity, there is a locally unstable infection-free equilibrium and a unique, globally asymptotically stable endemic equilibrium. If the control reproduction number is less than unity, the infection-free equilibrium is globally asymptotically stable

This paper is devoted to the study of semi-infinite optimization with nonsmooth data. We introduce the Arrow-HurwitczUzawa constraint qualification which is based on the Clarke subdifferential. Then, we derive a suitable Karush-Kuhn-Tucker type necessary optimality condition

In this paper, a revised measure-theoretical approach is applied for solving some classical optimal control problems. Indeed, the problem is converted into an optimization problem in measure space and then it is transformed into a finite dimensional nonlinear programming problem by using approximation scheme. At last, the nearly optimal control and trajectory functions are determined from the solution of the nonlinear optimization problem. A numerical example is given to demonstrate the efficiency of this method.

The aim of this paper is to establish the structure of C∗-algebra-valued b2-metric space and give some xed point theorems forself-maps with contractive or expansive conditions on such spaces. Asan application we investigate existence and uniqueness solution for atype of integral equation.

The notions of dualistic Geraghty Contraction is intoduced. A new fixed point theorem is proved in the settings of complete dualistic partial metric spaces. The counterpart theorem provided in partial metric spaces is retrieved as a particular case of our new results. We give example to prove that the contractive conditions in the statement of our new fixed point theorem can not be replaced by those contractive conditions in the statement of the partial metric counterpart fixed point theorem. Moreover, we give application of our fixed point theorem to show the existence of solution of integral equations.

The main aim of this paper is to construct an orthonormal wavelet on H2(D), the Hardy space of analytic functions on the open unit disc with square summable Taylor coefficients

We extend the notions of integration and differentiation to cover the class of functions taking values in topological vector spaces. We give versions of the Lebesgue-Nikodym Theorem and the Fundamental Theorem of Calculus in such a more general setting.