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In this paper, we generalize Nadler’s result by establishing the existence and uniqueness of coincidence and common fixed points of Nadler’s type set-valued mappings in ultrametric spaces. Examples are given to illustrate the results. As an application, well-posedness of a common fixed point problem is proved. The presented results generalize many known results in literature in the framework of ultrametric spaces.

<p>The purpose of this paper is to establish the existence and uniqueness of common fixed points of a family of self-mappings satisfying generalized rational contractive condition in 2-Banach spaces. An example is included to justify our results. We approximate the common fixed point by Mann and Picard type iteration schemes. Further, an application to well-posedness of the common fixed point problem is given. The presented results generalize many known results on 2-Banach spaces.</p>

Security is the rising concern of the wireless network as there are various forms of reonfigurable network that is arised from it. Wireless sensor network (WSN) is one such example that is found to be an integral part of cyber-physical system in upcoming times. After reviewing the existing system, it can be seen that there are less dominant and robust solutions towards mitigating the threats of upcoming applications of WSN. Therefore, this paper introduces a simple and cost-effective modelling of a security system that offers security by ensuring secure selection of clusterhead during the data aggregation process in WSN. The proposed system also makes construct a rule-set in order to learn the nature of the communication iin order to have a discrete knowledge about the intensity of adversaries. With an aid of simulation-based approach over MEMSIC nodes, the proposed system was proven to offer reduced energy consumption with good data delivery performance in contrast to existing approach.

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