A Relation-Theoretic Matkowski-Type Theorem in Symmetric Spaces

A Fatou-type Theorem for Harmonic Functions on Symmetric Spaces

A cone theoretic Krein-Milman theorem in semitopological cones

In this paper, a Krein-Milman  type theorem in $T_0$ semitopological cone is proved,  in general. In fact, it is shown that in any locally convex $T_0$ semitopological cone, every convex compact saturated subset is the compact saturated convex hull of its extreme points, which improves the results of Larrecq.

Vanishing Theorem for Irreducible Symmetric Spaces of Noncompact Type

We prove the following vanishing theorem. Let M be an irreducible symmetric space of noncompact type whose dimension exceeds 2 and M 6= SO0(2, 2)/SO(2)×SO(2). Let π : E → M be any vector bundle, Then any E−valued L harmonic 1-form over M vanishes. In particular we get the vanishing theorem for harmonic maps from irreducible symmetric spaces of noncompact type.

A Conjugacy Theorem for Symmetric Spaces

In this paper we prove that two Cartan subspaces of a semisimple symmetric pair (g, τ) are conjugate under G = Int(g) if and only if they are conjugate under (Gτ )0. Moreover we derive a double coset decomposition for G, which improves the results of Oshima and Matsuki.

FIXED POINT TYPE THEOREM IN S-METRIC SPACES

 A variant of fixed point theorem is proved in the setting of S-metric spaces