in this paper, we give a new fixed point theorem forweakly quasi-contraction maps in metric spaces. our results extend and improve some fixed point and theorems in literature.

The dimensions of the symmetry classes of tensors, associated with a certain cyclic subgroup of $m which is generated by a product of disjoint cycles is explicitly given in terms of the generalized Ramanujan sum. These dimensions can also be expressed as the Euler φ-function and the Möbius function.

The generalized state space of a commutative C-algebra, denoted SH(C(X)), is the set of positive unital maps from C(X) to the algebra B(H) of bounded linear operators on a Hilbert space H. C-convexity is one of several non-commutative analogs of convexity which have been discussed in this context. In this paper we show that a C-extreme point of SH(C(X)) satisfies a certain spectral condition on...

We study biharmonic hypersurfaces in a generic Riemannian manifold. We first derive an invariant equation for such hypersurfaces generalizing the biharmonic hypersurface equation in space forms studied in [16], [8], [6], [7]. We then apply the equation to show that the generalized Chen’s conjecture is true for totally umbilical biharmonic hypersurfaces in an Einstein space, and construct a (2-p...

This paper is devoted to the study of a broad class of problems in conic programming modeled via parameter-dependent generalized equations. In this framework we develop a secondorder generalized differential approach of variational analysis to calculate appropriate derivatives and coderivatives of the corresponding solution maps. These developments allow us to resolve some important issues rela...

We consider five different types of systems of generalized vector quasi-equilibrium problems and establish relationships among them by using different kinds of generalized pseudomonotonicities. We prove the existence of their solutions under lower semicontinuity for a family of multivalued maps involved in the formulation of these problems. The existence of solutions of these problems is also i...