Significant contribution to the Frankl's union-closed conjecture

A celebrated unresolved conjecture of Peter Frankl states that every finite union-closed collection of sets ($B$), with non-empty universe, admits an abundant element. The best result in the literature states that if $\mathrm{\mid }B\mathrm{\mid }=n$, then there exists $x$ in the universe of $B$ with frequency at least $$\frac{n-1}{{\log }_{2}n}\mathrm{.}$$ But $(n-1)\mathrm{/}(n{\log }_{2}n)\to 0$ as $n\rightarrow \infty$\mathrm{.}Inthispaper,weshowthatthereexistsaconstant$g>0$ such that for every $B$; there exists $x\in \mathtt{\text{U}}(B)$ such that $$\mathrm{\mid }{B}_x\mathrm{\mid }\ge g\mathrm{\mid }B\mathrm{\mid }$$ where $B_x=\{A\in B:x\in A\}$ and $$\mathtt{\text{U}}(B)=\bigcup _{A\in B}A\mathrm{.}$$