and Applied Analysis 3 Definition 1.10 see 5 . Let X,G be a G-metric space and f, g : X → X be given mappings. We say that f is a generalized weakly G-contraction mapping of type B with respect to g if for all x, y, z ∈ X, the following inequality holds: ψ ( G ( fx, fy, fz )) ≤ ψ ( G ( gx, gx, fy ) G ( gy, gy, fz ) G ( gz, gz, fx ) 3 ) − φGgx, gx, fy, Ggy, gy, fz, Ggz, gz, fx, 1.2

Let $mathfrak{F}$ be a formation and $G$ a finite group. A subgroup $H$ of $G$ is said to be weakly $mathfrak{F}_{s}$-quasinormal in $G$ if $G$ has an $S$-quasinormal subgroup $T$ such that $HT$ is $S$-quasinormal in $G$ and $(Hcap T)H_{G}/H_{G}leq Z_{mathfrak{F}}(G/H_{G})$, where $Z_{mathfrak{F}}(G/H_{G})$ denotes the $mathfrak{F}$-hypercenter of $G/H_{G}$. In this paper, we study the structur...

A subgroup H of a group G is called ss-quasinormal in G if there is a subgroup B of G such that G = HB and H permutes with every Sylow subgroup of B; H is called weakly s-permutable in G if there is a subnormal subgroup T of G such that G = HT and H ∩ T ≤ HsG, where HsG is the subgroup of H generated by all those subgroups of H which are s-permutable in G. We fix in every non-cyclic Sylow subgr...

A subgroup H is said to be s-permutable in a group G, if HP = PH holds for every Sylow subgroup P of G. If there exists a subgroup B of G such that HB = G and H permutes with every Sylow subgroup of B, then H is said to be SS-quasinormal in G. In this paper, we say that H is a weakly SS-quasinormal subgroup of G, if there is a normal subgroup T of G such that HT is s-permutable and H ∩ T is SS-...

Abstract. In this paper, we introduce generalized fuzzy weakly interior ideals of an ordered semigroup. We generalize fuzzy interior ideals of an ordered semigroup. We establish necessary and sufficient condition for a fuzzy set to be a generalized fuzzy weakly interior ideal. We establish three equivalent conditions for an ordered semigroup to be regular. We characterize semisimple ordered sem...

Let S be a topological semigroup acting on a topological space X. We develop the theory of (weakly) almost periodic functions on X, with respect to S, and form the (weakly) almost periodic compactifications of X and S, with respect to each other. We then consider the notion of an action of Son a Banach space, and on its dual, and after defining S-invariant means for such a space, we give a...