Journal of Advances in Applied Mathematics

8

Authors: Sanaa ElFadily, Abdelilah Kaddar, Khalid Najib

In this paper, we propose a model of mutual interactions between the economically active population and the economic growth. Our principal goal is to introduce a delayed equation of the active population evolution. The time delay, resulting from the recruitment processes, is incorporated in the effective labor demand. The dynamics are studied in terms of local stability and of the description of the Hopf bifurcation, is proven to exist as the delay (taken as a parameter of bifurcation) cross some critical value. Some numerical simulations are given to illustrate our theoretical results. Additionally we conclude with some remarks.

10

Authors: Lin-Chang Shen, Yue-Ying Yang, Wei-Mao Qian

In this paper, we give the explicit formulas for Neuman means of the second kind NGQ(a, b) and NQG(a, b), and find the best possible parameters αi, βi ∈ (0, 1)(i = 1, 2, 3, · · · , 6) such that the double inequalities α1Q(a, b) + (1 − α1)G(a, b) < NQG(a, b) < β1Q(a, b) + (1 − β1)G(a, b), α2 G(a, b) + 1 − α2 Q(a, b) < 1 NQG(a, b) < β2 G(a, b) + 1 − β2 Q(a, b) , α3Q(a, b) + (1 − α3)G(a, b) < NGQ(a, b) < β3Q(a, b) + (1 − β3)G(a, b), α4 G(a, b) + 1 − α4 Q(a, b) < 1 NGQ(a, b) < β4 G(a, b) + 1 − β4 Q(a, b) , α5Q(a, b) + (1 − α5)V (a, b) < NQG(a, b) < β5Q(a, b) + (1 − β5)V (a, b), α6Q(a, b) + (1 − α6)U(a, b) < NGQ(a, b) < β6Q(a, b) + (1 − β6)U(a, b), holds for all a, b > 0 with a 6= b, where G(a, b) and Q(a, b) are the classical geometric and quadratic means, V (a, b), U(a, b), NQG(a, b) and NGQ(a, b) are Yang and Neuman mean of the second kind.

12

Authors: Marta Demma, Peyman Salimi, Pasquale Vetro

We establish partial coupled fixed point and coupled fixed point results for mixed monotone mappings satisfying a generalized contractive condition in ordered partial metric spaces and ordered metric spaces. Our results generalize some interesting coupled fixed point theorems obtained in [T. G. Bhaskar and V. Lakshmikantham, “Fixed point theorems in partially ordered metric spaces and applications”, Nonlinear Anal., vol. 65, pp. 1379–1393, 2006].