Non Absolutely Convergent Integrals of Functions Taking Values in a Locally Convex Space

Non-absolutely Convergent Integrals in Metric Spaces

Strongly almost ideal convergent sequences in a locally convex space defined by Musielak-Orlicz function

In this article, we introduce a new class of ideal convergent sequence spaces using an infinite matrix, Musielak-Orlicz function and a new generalized difference matrix in locally convex spaces. We investigate some linear topological structures and algebraic properties of these spaces. We also give some relations related to these sequence spaces.

Singular values of convex functions of matrices

‎Let $A_{i},B_{i},X_{i},i=1,dots,m,$ be $n$-by-$n$ matrices such that $‎sum_{i=1}^{m}leftvert A_{i}rightvert ^{2}$ and $‎sum_{i=1}^{m}leftvert B_{i}rightvert ^{2}$  are nonzero matrices and each $X_{i}$ is‎ ‎positive semidefinite‎. ‎It is shown that if $f$ is a nonnegative increasing ‎convex function on $left[ 0,infty right) $ satisfying $fleft( 0right)‎ ‎=0 $‎, ‎then  $$‎2s_{j}left( fleft( fra...

A theory of non-absolutely convergent integrals in R with singularities on a regular boundary

Specializing a recently developed axiomatic theory of non-absolutely convergent integrals in R, we are led to an integration process over quite general sets A ⊆ R with a regular boundary. The integral enjoys all the usual properties and yields the divergence theorem for vector-valued functions with singularities in a most general form. Introduction. Consider an n-dimensional vector field ~v whi...

Harmonic functions in non-locally convex spaces