First, we show that a warped product of line with Riemannian manifold (fiber) is weakly conformally flat and quasi Einstein if only the fiber in which case Bach flat. Finally, characterize classify contact manifolds satisfying (and doubly weakly) quasi-Einstein ( $$\eta $$ -Einstein) conditions.

We recast the problem of calculating Vapnik-Chervonenkis (VC) density into one of counting types, and thereby calculate bounds (often optimal) on the VC density for some weakly o-minimal, weakly quasi-o-minimal, and P -minimal theories.

Families of maps on the lattice of all antichains of a finite bounded poset that extend the blocker, deletion, and contraction maps on clutters are considered. Influence of the parameters of the maps is investigated. Order-theoretic extensions of some principal relations for the set-theoretic blocker, deletion, and contraction maps on clutters are presented. 1. Introduction and preliminary. Let...

In this paper, the concept of generalized Jaggi-Berinde contraction multivalued maps in partially ordered metric spaces is introduced. A fixed point theorem for such maps is established. An example is given to support our main result. We investigate the stability of fixed points for a sequence of generalized Jaggi-Berinde contraction multivalued maps in partially ordered metric spaces. Our resu...

In this paper, first we prove common fixed point theorems for a pair of weakly compatible maps. Secondly, we prove a fixed point theorem for weakly compatible maps along with (CLRg) property. In fact, our results generalize the results of Z. Mustafa et al. [10]. 2000 AMS Classification: 47H10, 54H25

We prove a unique common fixed-point theorem for two pair of weakly compatible maps in a complete metric space, which generalizes the result of Brian Fisher by a weaker condition such as weakly compatibility instead of compatibility and contractive modulus instead of continuity of maps.