Hölder metric subregularity for multifunctions in type Banach spaces

Using the Borwein–Preiss variational principle and in terms of the proximal coderivative, we provide a new type of sufficient conditions for the Hölder metric subregularity and Hölder error bounds in a class of smooth Banach spaces. As an application, new characterizations for the tilt stability of Hölder minimizers are established.     

Matrix approaches to approximate solutions of variational inequalities in Hilbert spaces

A matrix approach to approximating solutions of variational inequalities in Hilbert spaces is introduced. This approach uses two matrices: one for iteration process and the other for regularization. Ergodicity and convergence (both weak and strong) are studied. Our methods combine new or well-known iterative methods (such as the original Mann’s method) with regularized processes involved regular matrices in the sense of Toeplitz.     

Reverse order law for generalized inverses of multiple operator product

In this paper, we consider the reverse order law for generalized inverses of operators on Hilbert spaces. We derive necessary and sufficient conditions for various inclusions concerning the reverse order law for generalized inverses of multiple operator product. We extend the finite dimensional results from (Wei M. Reverse order laws for generalized inverses of multiple matrix products. Linear Algebra Appl. 1999;293:13.) to infinite dimensional settings.     

Minimax theorems for set-valued maps without continuity assumptions

We introduce several classes of set-valued maps with new generalized convexity properties. We also obtain minimax theorems for set-valued maps which satisfy these convexity assumptions and which are not continuous. Our method consists of the use of a fixed point theorem for weakly naturally quasiconcave set-valued maps, defined on a simplex in a topological vector space, or of a constant selection of quasiconvex set-valued maps.     

Approximating a common zero of finite family of monotone operators in Hadamard spaces

In this paper, a common zero of a finite family of monotone operators is approximated in Hadamard spaces. Some applications in convex minimization and fixed point theory are also presented.