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A Common Fixed Point Theorem for Expansive Mappings under Strict Implicit Conditions on b-Metric Spaces

Mohamed Akkouchi — 2011

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica

In the setting of a b-metric space (see [Czerwik, S.: Contraction mappings in b-metric spaces Acta Math. Inform. Univ. Ostraviensis 1 (1993), 5–11.] and [Czerwik, S.: Nonlinear set-valued contraction mappings in b-metric spaces Atti Sem. Mat. Fis. Univ. Modena 46, 2 (1998), 263–276.]), we establish two general common fixed point theorems for two mappings satisfying the (E.A) condition (see [Aamri, M., El Moutawakil, D.: Some new common fixed point theorems under strict contractive conditions Math....

Optimality Conditions for a Nonlinear Boundary Value Problem Using Nonsmooth Analysis

Mohamed AkkouchiAbdellah BounabatManfred Goebel — 2003

Annales mathématiques Blaise Pascal

We study in this paper a Lipschitz control problem associated to a semilinear second order ordinary differential equation with pointwise state constraints. The control acts as a coefficient of the state equation. The nonlinear part of the equation is governed by a Nemytskij operator defined by a Lipschitzian but possibly nonsmooth function. We prove the existence of optimal controls and obtain a necessary optimality conditions looking somehow to the Pontryagin’s maximum principle. These conditions...

On generalized d'Alembert functional equation.

Mohamed AkkouchiAllal BakaliBelaid BouikhaleneEl Houcien El Qorachi — 2006

Extracta Mathematicae

Let G be a locally compact group. Let σ be a continuous involution of G and let μ be a complex bounded measure. In this paper we study the generalized d'Alembert functional equation D(μ)    ∫G f(xty)dμ(t) + ∫G f(xtσ(y))dμ(t) = 2f(x)f(y) x, y ∈ G; where f: G → C to be determined is a measurable and essentially bounded function.

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