Semigroups of transformations and endomorphisms have emerged as powerful algebraic frameworks to elucidate the underlying structures of graphs. By harnessing the principles of semigroup theory ...

The graph of y = f (x) where f (x) = x 2 is the same as the graph of y = x 2. Writing equations as functions in the form f (x) is useful when applying translations and reflections to graphs.

Motivated by work of Yu.L. Shmul'yan a pre-order and an equivalence relation on the set of operator-valued Schur class functions are introduced and the behavior of Redheffer linear fractional ...

In this paper, we will obtain new algebraic transformations of the 2 F 1 -hypergeometric functions. The main novelty in our approach is the interpretation of identities among 2 F 1 -hypergeometric ...