‎‎Set X = { M11‎, ‎M12‎, ‎M22‎, ‎M23‎, ‎M24‎, ‎Zn‎, ‎T4n‎, ‎SD8n‎, ‎Sz(q)‎, ‎G2(q)‎, ‎V8n}‎, where M11‎, M12‎, M22‎, ‎M23‎, ‎M24 are Mathieu groups and Zn‎, T4n‎, SD8n‎, ‎Sz(q)‎, G2(q) and V8n denote the cyclic‎, ‎dicyclic‎, ‎semi-dihedral‎, ‎Suzuki‎, ‎Ree and a group of order 8n presented by                                      V8n = < a‎, ‎b | a^{2n} = b^{4} = e‎, ‎ aba = b^{-1}‎, ‎ab^{...

We show that for every positive integer d, every downwards closed subtree T of d without terminal nodes and every finite weakly embedded subtree A of T there is a finite list of equivalence relations on Em(T ) with the property that for every other equivalence relation E on Em(T ) there is a strongly embedded subtree S ⊆ T of height ω, such that E Em(S) is equal to one of the equivalence relati...

Debnath and De La Sen introduced the notion of set valued interpolative Hardy-Rogers type contraction mappings on b-metric spaces proved that a complete space, whose all closed bounded subsets are compact, mapping has fixed point. This article presents generalizations above results by omitting assumption compact.

Let Tk be a family of all k-vertex trees. For T ⊆ Tk and a tree T , we write T → T if T contains at least one of the trees from T as a subtree, we write T 6→ T otherwise. Let ex(T ) be the smallest integer n, if such exists, such that for any tree T on at least n vertices T → T . It is shown that min{ex(T ) : T ⊆ Tk, |T | = q} = 2 log q−1 , where logq−1 is the q− 1 times iterated logarithm. In ...