On a theorem of G. D. Chakerian

Some Results on Baer's Theorem

Baer has shown that, for a group G, finiteness of G=Zi(G) implies finiteness of ɣi+1(G). In this paper we will show that the converse is true provided that G=Zi(G) is finitely generated. In particular, when G is a finite nilpotent group we show that |G=Zi(G)| divides |ɣi+1(G)|d′ i(G), where d′i(G) =(d( G /Zi(G)))i.

New best proximity point results in G-metric space

Best approximation results provide an approximate solution to the fixed point equation $Tx=x$, when the non-self mapping $T$ has no fixed point. In particular, a well-known best approximation theorem, due to Fan cite{5}, asserts that if $K$ is a nonempty compact convex subset of a Hausdorff locally convex topological vector space $E$ and $T:Krightarrow E$ is a continuous mapping, then there exi...

On a Covering Property of Convex Sets

Let [Kx, K2, ■ ■ ■ } be a class of compact convex subsets of euclidean M-space with the property that the set of their diameters is bounded. It is shown that the sets A, can be rearranged by the application of rigid motions so as to cover the total space if and only if the sum of the volumes of all the sets A, is infinite. Also, some statements regarding the densities of such coverings are prov...

On Tychonoff's type theorem via grills

‎Let ${X_{alpha}:alphainLambda}$ be a collection of topological spaces‎, ‎and $mathcal {G}_{alpha}$ be a grill on $X_{alpha}$ for each $alphainLambda$‎. ‎We consider Tychonoffrq{}s type Theorem for $X=prod_{alphainLambda}X_{alpha}$ via the above grills and a natural grill on $X$ ‎related to these grills, and present a simple proof to this theorem‎. ‎This immediately yields the classical theorem...

A Fixed Point Theorem in Generalized D-metric Spaces