Quotient spaces defined by linear relations

Quotient G-systems and Green\'s Relations

In this paper, we first introduce the concepts of G-systems, quotient G-systems and isomorphism theorems on G-systems of n-ary semihypergroups . Also we consider the Green's equivalences on G-systems and further in-vestigate some of their properties. A number of n-ary semihypergroups are constructed and presented as examples in this paper.

On difference sequence spaces defined by Orlicz functions without convexity

In this paper, we first define spaces of single difference sequences defined by a sequence of Orlicz functions without convexity and investigate their properties. Then we extend this idea to spaces of double sequences and present a new matrix theoretic approach construction of such double sequence spaces.  

Linear extensions of relations between vector spaces

LetX and Y be vector spaces over the same field K. Following the terminology of Richard Arens [Pacific J. Math. 11 (1961), 9–23], a relation F of X into Y is called linear if λF (x) ⊂ F (λx) and F (x) + F (y) ⊂ F (x+ y) for all λ ∈ K \ {0} and x, y ∈ X. After improving and supplementing some former results on linear relations, we show that a relation Φ of a linearly independent subset E of X in...

ε-weakly Chebyshev subspaces and quotient spaces

Norms on Quotient Spaces