In this paper, the concept of (∈,∈ ∨ qk)-fuzzy quasi-ideals of an ordered semigroup S is introduced by the ordered fuzzy points of S, which is a generalization of fuzzy quasi-ideal of S, and related properties are investigated. Furthermore, we introduce the concepts of prime and completely semiprime (∈,∈ ∨ qk)-fuzzy quasi-ideals of ordered semigroups, and characterize bi-regular ordered semigro...

In this manuscript the concept of hyperspace is revisited. The main purpose to study hyperconvergence and continuity orbital limit set functions for semigroup action on completely regular space. Some general facts Hausdorff Kuratowski are presented.

T then it is proved that (1) ) ( ) ( ) ( 0 1 2 A N A N A N A    (2) N0(A) = A2, N1(A) is a semiprime ideal of T containing A, N2(A) = A4 are equivalent, where No(A) = The set of all A-potent elements in T, N1(A) = The largest ideal contained in No(A), N2(A) = The union of all A-potent ideals. If A is a semipseudo symmetric ideal of a ternary semigroup then it is proved that N0(A) = N1(A) = N...

Given two multiplicative arithmetic functions, various conditions for their convolution, powers , and logarithms to be completely multiplicative, based on values at the primes, are derived together with their applications.