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3 Journal of Applied Analysis

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Strong convergence theorems for relatively quasi-nonexpansive mappings, variational inequality problems and systems of generalized mixed equilibrium problems

Shehu Y., Oguguo O.

Journal of Applied Analysis

2012

Vol. 18, nr 1

69-95

In this paper, we construct a new iterative scheme by hybrid methods to approximate a common element in the fixed points set of an infinite family of relatively quasi-nonexpansive mappings, the solutions set of a variational inequality problem and the solutions set of a system of generalized mixed equilibrium problems in a 2-uniformly convex real Banach space which is also uniformly smooth. Then, we prove strong convergence of the scheme to a common element of the three sets. We give several applications of our results in a Banach space. Our results extend many known recent results in the literature.

Approximation for fixed points of strict pseudo-contractions and solutions of equilibrium and optimization problems

Kang J., Su Y., Zhang H.

Journal of Applied Analysis

2010

Vol. 16, nr 1

1-13

In this paper, we introduce some iterative schemes for findin a common element of the set of fixed points of a k-strict pseudo-contractive mapping, the set of solutions of the variational inequality and the set of solutions of an equilibrium problem in a Hilbert space. The authors use the convex combination technique to show that the iterative sequences converge strongly to a common element of the three sets. The results of this paper extend and improve the results of Y. Su et al. [9], S. Plubtieng and R. Punpaeng [7], X. Qin et al. [8] and S. Takahashi and W. Takahashi [10].

A quasistatic contact problem with slip dependent coefficient of friction for elastic materials

Corneschi C., Hoarau-Mantel T.-V. T.-V., Sofonea M.

Journal of Applied Analysis

2002

Vol. 8, nr 1

63-82

We consider a mathematical model which describes the frictional contact between a deformable body and an obstacle, say a foundation. The body is assumed to be linear elastic and the contact is modeled with a version of Coulomb's law of dry friction in which the normal stress is prescribed on the contact surface. The novelty consists here in the fact that we consider a slip dependent coefficient of friction and a quasistatic process. We present two alternative yet equivalent formulations of the problem and establish existence and uniqueness results. The proofs are based on a new result obtained in [10] in the study of evolutionary variational inequalities.