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Abstract In the current paper, a generalized Montgomery identity is obtained with the help of Taylor’s formula on time scales. The obtained identity is used to establish Ostrowski inequality, mid-point inequality, and trapezoid inequality. Moreover, the weighted versions of generalized Montgomery identity and respective Ostrowski inequality are also discussed. Special cases are obtained for different time scales to obtain new and existing results.

The q-symmetric analogues of Hölder, Minkowski, and power mean inequalities are presented in this paper. The obtained inequalities along with a Montgomery identity involving q-symmetric integrals are used to extend some Ostrowski-type inequalities. The q-symmetric derivatives of the functions involved in these Ostrowski-type inequalities are convex or s-convex. Moreover, some Hermite–Hadamard inequalities for convex functions as well as for s-convex functions are also acquired with the help of q-symmetric calculus in the present work. Some examples are included to support the effectiveness of the proved results.

In the paper we extend some Hardy and Littlewood type inequalities on time scales for the function of n variables. Special cases of obtained results include generalized Wirtinger, Hardy and Littlewood type inequalities.

In the present paper, q-fractional integral operators are used to construct quantum analogue of Ostrowski type inequalities for the class of s-convex functions. The limiting cases include the nonfractional existing cases from literature. Specially, Ostrowski type inequalities for q-integrals and Ostrowski type inequalities for convex functions are deduced.

The new outcomes of the present paper are q-analogues (q stands for quantum calculus) of Hermite-Hadamard type inequality, Montgomery identity, and Ostrowski type inequalities for s-convex mappings. Some new bounds of Ostrowski type functionals are obtained by using Hölder, Minkowski, and power mean inequalities via quantum calculus. Special cases of new results include existing results from the literature.

Abstract In the paper, some variants of Montgomery identity with the help of delta and nabla integrals are established which are useful to produce Montgomery identity involving alpha diamond integrals for function of two variables. The aforementioned identity is discussed in discrete, continuous, quantum calculus as well and employed to obtain Ostrowski type inequality for monotonically increasing function with respect to both parameters.

In this study, we extend some “sneak-out” inequalities on time scales for a function depending on more than one parameter. The results are proved by using the induction principle and time scale version of Minkowski inequalities. In seeking applications, these inequalities are discussed in classical, discrete, and quantum calculus.

In this paper, Hölder, Minkowski, and power mean inequalities are used to establish Ostrowski type inequalities for s-convex functions via h-calculus. The new inequalities are generalized versions of Ostrowski type inequalities available in literature.

The departments of transportation worldwide are facing various challenges despite introducing and incorporating various vehicular features. One of such challenges is to make vehicles autonomous, intelligent, and capable of self-learning to evolve their knowledge repository. In this paper, human cognition is proposed to be implemented in vehicles so that they can perform human-like decisions. Therefore, the process of vehicular route decision is debated cognitively in order to provide route information intelligently. The in-vehicle routes provided by the GPS are not optimal and lack on-demand user requirements. GPS connectivity issues, in certain conditions, make it difficult for vehicles to take real-time decisions. This leads to the idea of self-decision by the vehicle controller. We propose a cognitive framework for vehicles to make self-decisions that use cognitive memory for storing route experiences. The framework strengthens the existing in-vehicle route finding capability and its provision in a more realistic manner. The user is provided with all available route-related information that is required for the journey. In addition, the route episodes are learned, stored, and accessed inside the cognitive memory for an optimal route provision. The vehicle learns about the routes and matures with route-experience by itself with the passage of time. In simulations, fuzzy modeling is used to validate the impact of cognitive parameters over static/conventional parameters. Moreover, artificial neural networks are used to minimize the error rate in learning to achieve cognitive route decisions. The proposed in-vehicle cognitive framework outperforms the existing route provision system that is inadequate and provokes the user's anxieties during driving. Besides, the proposed scheme gradually gets mature in delivering optimal as well as latest route-related information.

In this paper, Jensen’s inequality and Fubini’s Theorem are extended for the function of several variables via diamond integrals of time scale calculus. These extensions are used to generalize Hardy-type inequalities with general kernels via diamond integrals for the function of several variables. Some Hardy Hilbert and Polya Knop type inequalities are also discussed as special cases. Classical and new inequalities are deduced from the main results using special kernels and particular time scales.

Internet of Things (IoT) is an emerging technology that offers promising solutions to modernize the traditional systems. It accords promising result in crystallizing smart cities, smart homes, smart industries, and smart environment. This article presents the smart waste management architecture for smart cities and efficient routing technique considering least delay for the architecture. In wireless sensor networks, end-to-end delay is one of the important Quality of Services (QoS) parameter to overcome delay in data communication. In this article, we consider end-to-end delay minimization in smart waste management application. The term “end-to-end delay” is defined as the total time taken by a single packet to reach the destination node. The proposed scheme considers the interference level, the length of the routing path, and the number of hops along the path. The simulation results show that the proposed scheme outperforms current schemes.

The paper proposes a sensors platform to control a barrier that is installed for vehicles entrance. This platform is automatized by image-based license plate recognition of the vehicle. However, in situations where standardized license plates are not used, such image-based recognition becomes non-trivial and challenging due to the variations in license plate background, fonts and deformations. The proposed method first detects the approaching vehicle via ultrasonic sensors and, at the same time, captures its image via a camera installed along with the barrier. From this image, the license plate is automatically extracted and further processed to segment the license plate characters. Finally, these characters are recognized with the help of a standard optical character recognition (OCR) pipeline. The evaluation of the proposed system shows an accuracy of 98% for license plates extraction, 96% for character segmentation and 93% for character recognition.