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In this paper, we introduce a new class of contractive mapping in intuitionistic fuzzy metric space (IFMS). We establish fixed point theorems under such contractive mapping in complete IFMS and prove a common fixed point theorem for weakly compatible mappings under ϕ-contractive conditions in IFMS.

Dealing with the threats of vector-borne diseases necessitates robust disease surveillance systems. The gathered information from surveillance studies is used to evaluate the effectiveness of control measures. It also guides the allocation of resources within the healthcare system. The disease surveillance data also identify high-risk populations or geographic areas to target interventions. Because of the importance of surveillance in decision-making and its timely requirement, real-time data collection is vital. A few advantages of real-time data collection apps are building powerful digital forms, exporting data for quick analysis in various formats, and being open-source. These apps automate data collection and transfer to an online server even without an internet connection. While collecting disease surveillance data digitally one crucial aspect lacking is data quality. This paper aims to present the importance of dashboards that includes paradata in improving data quality using real-time data collection tools in disease surveillance. Various types of paradata such as timestamps, geo-referencing, audio recording and so on help enhance the quality of data and can help monitor and evaluate surveillance staff. The outcomes of the paradata analysis may lead to the retraining of the surveillance team and even re-planning of surveillance. Undoubtedly, real-time data collection is the way of the future in any field-based study, and studies should be planned in conjunction with paradata to ensure that high-quality data are recorded.

The aim of this paper is to obtain a fixed point theorem for mappings satisfying a generalized ($$\psi , \phi$$)-weak contractive type condition in a complete metric space. Moreover, our result also generalizes some well known theorems in the literature.

We generalize the Caristi fixed point theorem by employing a weaker form of continuity and show that contractive type mappings that satisfy the conditions of our theorem provide new solutions to the Rhoades? problem on continuity at fixed point. We also obtain a Meir-Keeler type fixed point theorem which gives a new solution to the Rhoades? problem on the existence of contractive mappings that admit discontinuity at the fixed point. We prove that our theorems characterize completeness of the metric space as well as Cantor?s intersection property.

We obtain a Meir–Keeler type fixed-point theorem which gives a new solution to the Rhoades’ problem on the existence of contractive mappings that admit discontinuity at the fixed point. Meir–Keeler type solutions of the Rhoades’ problem have not been reported in literature before this. Presenting a new approach, we give another solution to this problem using the set of simulation functions. To emphasize the importance of our theoretical results, we obtain two applications of the main results with some illustrative examples.

In this paper, a fixed point theorem for multi-valued mappings on a complete metric space is established taking a general contractive condition which generalizes several contractive conditions. Many generalizations of some well known results are also obtained as corollaries. Further, we give an application to the existence and uniqueness of solutions for certain classes of functional equations arising in dynamic programming.

A Distributed Denial of Service (DDoS) attack try to make services or resources unavailable to legitimate customers of that service or resource. These attacks are relatively easy to perform and extremely hard to detect in early stages. Different types of detection techniques were proposed by researcher to detect DDoS in its early stages but due to closed nature of networking devices, no promising results were produced. However, with the advents of Software-Defined Network (SDN), situation has changed. SDN is a cutting edge technology, which separates control plane from data plane. Its features, like programmability and centralized view of network, can be used to overcome the difficulties faced by researches. In this paper, we discussed different detection techniques of DDoS and how these techniques can be made more effective by leveraging the unique features of SDN.

In the present paper, we extend the concept ofWeak Reciprocal Continuity for a hybrid pair of single-valued and multi-valued maps and introduce (T; f)-completeness of the space. Further, we establish some results on the existence of coincidence and fixed points for the hybrid pair of maps. Our results generalize several well known results available in the literature

In this paper we introduce a weighted retro Banach frame for a discrete signal space. Necessary and sufficient condition for the existence of weighted retro Banach frames is obtained. Construction of weighted retro Banach frames from bounded linear operator is discussed. A Paley-Wiener type perturbation result for weighted retro Banach frame in Banach space setting is given.

G-atomic decompositions for Banach spaces with respect to a model space of sequences have been introduced and studied as a generalization of atomic decompositions. Examples and counter example have been provided to show its existence. It has been proved that an associated Banach space for G-atomic decomposition always has a complemented subspace. The notion of a representation system is introduced and exhibits its relation with G-atomic decomposition. Also It has been observed that G-atomic decompositions are exactly compressions of Schauder decompositions for a larger Banach space. We give a characterization for finite G-atomic decomposition in terms of finite-dimensional expansion of identity. Keywords: complemented coefficient spaces, finite-dimensional expansion of identity, G-atomic decomposition, representation system.

Vedāga Jyotia is an oldest hand book on Vedic astronomical observations in India. This small text, consists of a few pages of Sanskrit verses, has its historical importance in astronomy and mathematics because of the position of solstices and equinoxes recorded therein. This oldest astronomical treatise is a collection of seventy nine verses in two recensions. The first recensionknown as, Ārca- Jyotia, and consists of thirty six verses from Rigveda and the second recensionknown as, Yājua -Jyotia, which consists of forty three verses from Yajurveda. However, most of the verses are common in both recensions. This treatise ‘Vedāga Jyotia’ on mathematical astronomy was authored by ‘Rishi’ Lagadha probably in latter Vedic period. In Vedāga Jyotia, mainly the motions of the Moon and the Sun were summarized to perform the Vedic rituals and periodic sacrifices at particular times. The Vedāga Jyotia preserves the traditional knowledge of mathematical sciences, which was developed during Vedic period. The achievement in astronomy was based on mathematical calculations. The object of this paper is to bring out the mathematical rules used in Vedāga Jyotia for astronomical calculations, time period and place of observations, division of time and description of some the important studies of Vedāga Jyotia in chronological order.