We introduce generalized Priestley quasi-orders and show that subalgebras of bounded distributive meet-semilattices are dually characterized by means of generalized Priestley quasi-orders. This generalizes the well-known characterization of subalgebras of bounded distributive lattices by means of Priestley quasiorders (Adams, Algebra Univers 3:216–228, 1973; Cignoli et al., Order 8(3):299– 315,...

In this paper we study left and right 4-Engel elements of a group. In particular, we prove that 〈a, a〉 is nilpotent of class at most 4, whenever a is any element and b are right 4-Engel elements or a are left 4-Engel elements and b is an arbitrary element of G. Furthermore we prove that for any prime p and any element a of finite p-power order in a group G such that a ∈ L4(G), a, if p = 2, and ...

In this paper, we introduce the concept of generalized quasi-contractions in the setting of cone $b$-metric spaces over Banach algebras. By omitting the  assumption of normality we establish common fixed point theorems for the generalized quasi-contractions  with the spectral radius $r(lambda)$ of the quasi-contractive constant vector $lambda$ satisfying $r(lambda)in [0,frac{1}{s})$  in the set...

In this paper, we introduce and study a new class of generalized mixed quasi-variational-like inequalities. Using the auxiliary principle technique, we construct a new iterative algorithm for finding the approximate solutions of the generalized mixed quasi-variational-like inequality. An existence result of solutions for the generalized mixed quasi-variational-like inequality and the convergenc...

A rigidity result for a class of compact generalized quasi-Einstein manifolds with constant scalar curvature is obtained. Moreover, under some geometric assumptions, the non-compact case also proved. Considering non curvature, we characterize which conformal to Euclidean space and show that there exist two classes complete manifolds, are obtained by considering potential functions factors eithe...