Security issues in Vehicular Ad-Hoc Networks (VANETs) are important because of its diverse implications in safety related and congestion avoidance applications. A critical security problem in VANET is injection of false data, i.e. an attacker propagates false information to disrupt the behavior of drivers. Most of VANET applications are time critical and depend on the reliable position information in the safety messages received from the neighboring nodes. Disseminating incorrect position information in the safety message has severe impact on the performance, reliability and security of VANET applications. In this paper, we propose a distributed solution to detect malicious nodes propagating incorrect position information. This solution is based on series of verifications such as acceptance range verification, maximum allowable speed check, maximum density check, speed consistency verification and time interval substantiation computed by fixed Road Side Units (RSUs). In this approach, each RSU performs some set of logical operations to validate the legitimacy of positions of nodes sending safety messages. We have evaluated the proposed approach in both simulated and realistic scenario. Experimental results prove the validity of the proposed detection approach.
In this note a fixed point theorem for expansion mappings is established in a complete metric space under certain conditions. Further a common fixed point theorem for pair of weakly compatible expansion mappings is established. In this theorem the completeness of space is replaced with a set of four alternative conditions for functions satisfying implicit relations. These theorems extend and improve results of S. M. Kang [4], M. A. Khan et al. [5], B. E. Rhoades [11] and T. Taniguchi [12].
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