Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
This paper is concerned with weighted pseudo almost automorphic functions, which are more general and complicated than weighted pseudo almost periodic functions. Using these properties, we establish an existence and uniqueness theorem for pseudo almost automorphic mild solutions to semilinear differential equations in a Banach spaces which extends known results.
ISSN: 0362-546X

hal-00617634
https://hal.archives-ouvertes.fr/hal-00617634

Éditeur(s) : HAL CCSD
Résumé : International audience
In this paper, we prove a new composition theorem for asymptotically antiperiodic and weighted pseudo antiperiodic functions. We also give some sufficient conditions to ensure invertibility of convolution operators in the space of antiperiodic functions. Then we prove the existence and uniqueness of asymptotically antiperiodic mild solutions to some fractional functional integro-differential equations in a Banach space using the Banach's fixed point theorem.
African Diaspora Journal of Mathematics

hal-01678067
https://hal.archives-ouvertes.fr/hal-01678067

Éditeur(s) : HAL CCSD Yokohama
Résumé : International audience
We make use of the viscosity technique to develop a convergent method for approximating a common element of the set of fixed points of a demicontractive operator and the set of solutions of a monotone equilibrium problem. The proposed algorithm is obtained by coupling a modified hybrid steepest descent method with the extragradient algorithm. Under mild conditions, the strong convergence of the sequences generated by the algorithm is obtained. Using this result we obtain two corollaries which improve or develop several corresponding results in this field.
Journal of Nonlinear and Convex Analysis

hal-00779988
https://hal.univ-antilles.fr/hal-00779988

Éditeur(s) : HAL CCSD Springer Verlag
Résumé : International audience
We consider a bilevel problem involving two monotone equilibrium bifunctions and we show that this problem can be solved by a simple proximal method. Under mild conditions, the weak convergence of the sequences generated by the algorithm is obtained. Using this result we obtain corollaries which improve several corresponding results in this field.
ISSN: 0925-5001

hal-00776657
https://hal.univ-antilles.fr/hal-00776657
DOI : 10.1007/s10898-009-9476-1

Éditeur(s) : HAL CCSD Elsevier
Résumé : International audience
Two splitting procedures for solving equilibrium problems involving the sum of two bifunctions are proposed and their convergence is established under mild assumptions.
Journal of Mathematical Analysis and applications

hal-00779982
https://hal.univ-antilles.fr/hal-00779982
DOI : 10.1016/j.jmaa.2009.06.005

Éditeur(s) : HAL CCSD Hindawi Publishing Corporation
Résumé : International audience
This paper is concerned with the study of a penalization-gradient algorithmfor solving variational inequalities, namely, find x ∈ C such that Ax, y − x ≥ 0 for all y ∈ C, where A : H → H is a single-valued operator, C is a closed convex set of a real Hilbert space H. Given Ψ : H → ∪ { ∞} which acts as a penalization function with respect to the constraint x ∈ C, and a penalization parameter βk, we consider an algorithm which alternates a proximal step with respect to ∂Ψ and a gradient step with respect to A and reads as xk I λkβk∂Ψ −1 xk−1 − λkAxk−1 . Under mild hypotheses, we obtain weak convergence for an inverse strongly monotone operator and strong convergence for a Lipschitz continuous and strongly monotone operator. Applications to hierarchical minimization and fixed-point problems are also given and the multivalued case is reached by replacing themultivalued operator by its Yosida approximatewhich is always Lipschitz continuous.
ISSN: 0161-1712

hal-00776654
https://hal.univ-antilles.fr/hal-00776654
https://hal.univ-antilles.fr/hal-00776654/document
https://hal.univ-antilles.fr/hal-00776654/file/305856.pdf
DOI : 10.1155/2011/305856