Let G = (V,E) be a connected undirected graph. For any vertex v ∈ V , the closed neighborhood of v is N [v] = {v} ∪ {u ∈ V | uv ∈ E }. For S ⊆ V , the closed neighborhood of S is N [S] = ⋃ v∈S N [v]. The subgraph weakly induced by S is 〈S〉w = (N [S], E ∩ (S × N [S])). A set S is a weakly-connected dominating set of G if S is dominating and 〈S〉w is connected. The weakly-connected domination numb...

we introduce a two generated weakly branch contracting automaton group $g$ which is generated by a two state automaton on a three letter alphabet. using its branch structure and the finiteness nature of a sequence of its factor groups we compute the order of some of these factors. furthermore some algebraic properties of $g$ are detected .

in this paper, the notion of cyclic $varphi$-contraction in fuzzymetric spaces is introduced and a fixed point theorem for this typeof mapping is established. meantime, an example is provided toillustrate this theorem. the main result shows that a self-mappingon a g-complete fuzzy metric space has a unique fixed point if itsatisfies the cyclic $varphi$-contraction. afterwards, some results inco...

for a finite group $g$‎, ‎we study the total character $tau_g$‎ ‎afforded by the direct sum of all the non-isomorphic irreducible‎ ‎complex representations of $g$‎. ‎we resolve for several classes of‎ ‎groups (the camina $p$-groups‎, ‎the generalized camina $p$-groups‎, ‎the groups which admit $(g,z(g))$ as a generalized camina pair)‎, ‎the problem of existence of a‎ ‎polynomial $f(x) in mathbb...

Banach contraction principle is a fundamental result in fixed point theory and has been applied and extended in many different directions. In 2002, Branciari [3] obtained a fixed point theorem for a single mapping satisfying an analogue of Banach’s contraction principle for an integral type inequality. Aliouche [2] established a common fixed point theorem for weakly compatible mappings in symme...

An interesting observation is that most pairs of weakly homogeneous mappings do not possess strongly monotonic property, which one the key conditions to ensure unique solvability generalized variational inequality. This paper focuses on studying uniqueness and inequality with a pair mappings. By using weaker condition than strong monotonicity some additional conditions, we achieve several resul...