We provide a local convergence analysis for Secant– like algorithm for solving nonsmooth variational inclusions in Banach spaces. An existence–convergence theorem and an improvement of the ratio of convergence of this algorithm are given under center–conditioned divided difference and Aubin’s continuity concept. Our result compare favorably with related obtained in [16].

Under the lack of the condition , some new convergence and stability theorems of Mann and Ishikawa iterative processes with errors for solutions to variational inclusions involving accretive mappings in real reflexive Banach spaces are established. The main results of this paper extend and improve the corresponding results obtained by Chang, Ding, Hassouni and Moudafi, Huang, Kazmi, Noor, Siddi...

We present a new result for the local convergence of Newton–type method to a unique solution of a nonsmooth subanalytic variational inclusions in finite dimensional spaces. Under a center–type conditions [1]–[4] and using the same or less computational cost, we extend the applicability of Newton’s method [8], [10]. MSC 2010. 65K10, 65G99, 65H10, 65B05, 47H04, 49M15, 47H17, 14P15.

Based on the notion of A−maximal relaxed accretiveness, the convergence analysis of the over-relaxed proximal point algorithm in the context of the approximating the solutions of a class of nonlinear variational inclusions is explored. Moreover, some results on the general firm nonexpansiveness are also investigated. The obtained results are general and application-oriented in nature.

In this paper we study parametric evolution inclusions of the subdifferential type and their applications to the sensitivity analysis of nonlinear, infinite dimensional optimal control problems. The parameter appears in all the data of the problem, including the subdifferential operator. First we establish several continuity results for the solution multifunction of the subdifferential inclusio...

We propose new iterative schemes for finding the common element of the set of common fixed points of countable family of nonexpansive mappings, the set of solutions of the variational inequality problem for relaxed cocoercive and Lipschitz continuous, the set of solutions of system of variational inclusions problem, and the set of solutions of equilibrium problems in a real Hilbert space by usi...

The matrix variational Padé approximant and its generalization to elastic wave scattering are discussed. Predictions of the method for the scattering of a longitudinal plane wave are compared with the exact scattering from spherical voids and inclusions. Its predictions are also compared to those of the first and second Born approximations and to the standard matrix Padé approximant based on th...

The eeective energy of a mixture of two elastic materials in a thin lm is characterized using Gamma-limit techniques. For cylindrical shaped inclusions it is shown that 3D-2D asymptotics and optimal design commute from a variational viewpoint. Regularity of local minimizers for the resulting design is addressed.

We consider first order periodic differential inclusions in R . The presence of a subdifferential term incorporates in our framework differential variational inequalities in R . We establish the existence of extremal periodic solutions and we also obtain existence results for the “convex” and “nonconvex”problems.

In this paper, we consider a more general form of variational inclusions, called generalized variational inclusion (for short, GVI). In connection with GVI, we also consider a generalized resolvent equation with H-resolvent operator, called H-resolvent equation (for short, H-RE). We suggest iterative algorithms to compute the approximate solutions of GVI and H-RE. The existence of a unique solu...