Our aim in this article is to study the class of so-called $$\rho -$$ paraconvex multifunctions from a Banach space X into subsets another Y. These are defined relation with modulus function :X\rightarrow [0,+\infty )$$ satisfying some suitable conditions. This generalizes $$\gamma >1$$ introduced and studied by Rolewicz, eighties subsequently A. Jourani others authors. We establish regular pro...

This work presents an alternative formulation of resolvent analysis based on the calculus variations. The proposed circumvents reliance inversion linear operator and is inherently compatible with any arbitrary choice norm. Several examples are presented which highlight analytical numerical advantages limitations formulation.

The -pseudospectrum of a square matrix A is the set of eigenvalues attainable when A is perturbed by matrices of spectral norm not greater than . The pseudospectral abscissa is the largest real part of such an eigenvalue, and the pseudospectral radius is the largest absolute value of such an eigenvalue. We find conditions for the pseudospectrum to be Lipschitz continuous in the setvalued sense ...

In this paper, we consider a new class of quasi variational inequalities involving three operators, which is called the extended general quasi variational inequality. It is shown that the extended general quasi variational inequalities are equivalent to the fixed problems. This equivalence is used to suggest and analyze some iterative methods for solving the extended general quasi variational i...