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Approximate controllability by birth control for a nonlinear population dynamics model

Otared Kavian, Oumar Traoré (2011)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we analyse an approximate controllability result for a nonlinear population dynamics model. In this model the birth term is nonlocal and describes the recruitment process in newborn individuals population, and the control acts on a small open set of the domain and corresponds to an elimination or a supply of newborn individuals. In our proof we use a unique continuation property for the solution of the heat equation and the Kakutani-Fan-Glicksberg fixed point theorem.

Approximate controllability by birth control for a nonlinear population dynamics model

Otared Kavian, Oumar Traoré (2011)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper we analyse an approximate controllability result for a nonlinear population dynamics model. In this model the birth term is nonlocal and describes the recruitment process in newborn individuals population, and the control acts on a small open set of the domain and corresponds to an elimination or a supply of newborn individuals. In our proof we use a unique continuation property for the solution of the heat equation and the Kakutani-Fan-Glicksberg fixed point theorem.

Approximating common fixed points of asymptotically nonexpansive mappings by composite algorithm in Banach spaces

Xiaolong Qin, Yongfu Su, Meijuan Shang (2007)

Open Mathematics

Let E be a uniformly convex Banach space and K a nonempty convex closed subset which is also a nonexpansive retract of E. Let T 1, T 2 and T 3: K → E be asymptotically nonexpansive mappings with k n, l n and j n. [1, ∞) such that Σn=1∞(k n − 1) < ∞, Σn=1∞(l n − 1) < ∞ and Σn=1∞(j n − 1) < ∞, respectively and F nonempty, where F = x ∈ K: T 1x = T 2x = T 3 x = xdenotes the common fixed points set of T 1, T 2 and T 3. Let α n, α′ n and α″ n be real sequences in (0, 1) and ∈ ≤ α n, α′ n, α″...

Approximation methods for solving the Cauchy problem

Cristinel Mortici (2005)

Czechoslovak Mathematical Journal

In this paper we give some new results concerning solvability of the 1-dimensional differential equation y ' = f ( x , y ) with initial conditions. We study the basic theorem due to Picard. First we prove that the existence and uniqueness result remains true if f is a Lipschitz function with respect to the first argument. In the second part we give a contractive method for the proof of Picard theorem. These considerations allow us to develop two new methods for finding an approximation sequence for the solution....

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