For any non-trivial convex and bounded subset C of a Banach space, we show that outside σ-porous the space non-expansive mappings → C, all have maximal Lipschitz constant one witnessed locally at typical points C. This extends result Bargetz author from separable spaces to proof given is completely independent. We further establish fine relationship between classes exceptional sets involved in ...

Soil is naturally occurring material that is used for the construction of structures except the surface layers of pavements. This naturally occurring soil may not suit the design requirements of ongoing project. So, soil is to be prepared to meet the requirements called soil stabilization. Stabilization is the process of blending of different soils or mixing of additives to a soil to improve ch...

At present paper, we establish the existence of pullback $mathcal{D}$-attractor for the process associated with non-autonomous partly dissipative reaction-diffusion equation in $L^2(mathbb{R}^n)times L^2(mathbb{R}^n)$. In order to do this, by energy equation method we show that the process, which possesses a pullback $mathcal{D}$-absorbing set, is pullback $widehat{D}_0$-asymptotically compact.

we say that a finite group $g$ is conjugacy expansive if for anynormal subset $s$ and any conjugacy class $c$ of $g$ the normalset $sc$ consists of at least as many conjugacy classes of $g$ as$s$ does. halasi, mar'oti, sidki, bezerra have shown that a groupis conjugacy expansive if and only if it is a direct product ofconjugacy expansive simple or abelian groups.by considering a character analo...