More on Reverse Triangle Inequality in Inner Product Spaces

Refining some results of S. S. Dragomir, several new reverses of the generalized triangle inequality in inner product spaces are given. Among several results, we establish some reverses for the Schwarz inequality. In particular, it is proved that if $a$ is a unit vector in a real or complex inner product space $(H;)$, $r, s>0, p\in(0,s], D=\{x\in H,\|rx-sa\|\leq p\}, x_1, x_2\in D-\{0\}$ and $\alpha_{r,s}=\min\{\frac{r^2\|x_k\|^2-p^2+s^2}{2rs\|x_k\|}: 1\leq k\leq 2 \}$, then $$\frac{\|x_1\|\|x_2\|-Re}{(\|x_1\|+\|x_2\|)^2}\leq \alpha_{r,s}.$$Comment: 12 page

Fingerprint Based Hot Water Distribution System

This paper presents a modelling technique and an optimal scheme for automated hot water distribution which will be possible to distribute the HOT water equally to all candidates in hostels, so that everyone will get the equal amount of hot water. In urban areas, wastage of water and loss of electricity has become the serious problem. To minimize this problem, we can use this distribution system in order to reduce the wastage of water and save the electricity. The limitations to this model is distribution losses which ranges from 10%-40% of annual hot water energy consumption, depending upon factors such as hot water use quantity and patterns. Critical factors that affect the magnitude of the distribution loss include the layout of the distribution system and the magnitude and pattern of hot water loads within the hostels. This technique allows to allocate sufficient amount of water to the authenticated user by using biometric module and also control the flow of water and pressure

COMMON FIXED POINT THEOREMS INVOLVING C-CLASS FUNCTIONS IN G-METRIC SPACES

The purpose of this paper is to prove some common fixed point theorems using the concept of C class function in G-metric spaces. Moreover, some examples are presented to illustrate the validity of our results