This paper deals with the study of mixed variational-like inclusions involving Yosida approximation operator (MVLIYAO) and η-proximal mapping in Banach spaces. It is investigated that equivalent to fixed point problems Using this equivalence, a new iterative algorithm proposed find solution (MVLIYAO). A numerical example provided support our main result by using MATLAB program.

In this paper, we survey recent progress on the constructive theory of the Feynman operator calculus. We first develop an operator version of the Henstock-Kurzweil integral, and a new Hilbert space that allows us to construct the elementary path integral in the manner originally envisioned by Feynman. After developing our time-ordered operator theory we extend a few of the important theorems of...

Exact-diagonalization results for Kondo nanoclusters alloyed with mixed-valence impurities show that tuning the energy spacing D drives the system from the Kondo to the Ruderman-Kittel-Kasuya-Yosida (RKKY) regime. The interplay of D and disorder gives rise to a D versus concentration T=0 phase diagram very rich in structure. The parity of the total number of electrons alters the competition bet...

We study a posteriori error estimates for the numerical approximations of state constrained optimal control problems governed by convection diffusion equations, regularized by Moreau-Yosida and Lavrentiev-based techniques. The upwind Symmetric Interior Penalty Galerkin (SIPG) method is used as a discontinuous Galerkin (DG) discretization method. We derive different residual-based error indicato...

A new type of approximating curve for finding a particular zero of the sum of two maximal monotone operators in a Hilbert space is investigated. This curve consists of the zeros of perturbed problems in which one operator is replaced with its Yosida approximation and a viscosity term is added. As the perturbation vanishes, the curve is shown to converge to the zero of the sum that solves a part...

Moreau-Yosida and Lavrentiev type regularization methods are considered for nonlinear optimal control problems governed by semilinear parabolic equations with bilateral pointwise control and state constraints. The convergence of optimal controls of the regularized problems is studied for regularization parameters tending to infinity or zero, respectively. In particular, the strong convergence o...

We show that the paradigmatic Ruderman–Kittel–Kasuya–Yosida (RKKY) description of two local magnetic moments coupled to propagating electrons breaks down in helical Luttinger Liquids when the electron interaction is stronger than some critical value. In this novel regime, the Kondo effect overwhelms the RKKY interaction over all macroscopic inter-impurity distances. This phenomenon is a direct ...