Aim and Scope

Through this research article we prove parameterized inequality of fractional Hermite-Hadamard type. So, we acquired many results of Hermite-Hadamard type of inequalities.

This paper includes new versions of generalized Fejér-Hadamard (FH) type fractional integral inequalities (FIIs) for exponentially (p,h)-convex functions. We utilize an extracted generalized fractional integral operator (FIO) involving Mittag-Leffler function (MLF) which contains a monotone increasing function. Some special already published results are deduced from the presented results.

The s-convex functions of first kind and of second kind are well known functions. We would use recently introduced notion of s−convex functions of mixed kind and we would call it (s,r)−convex function. It would generalize the notion of first kind and second kind convexity in the sense that both kinds of convexities would be obtained easily by imposing certain specific conditions on it. We would state generalization of Hermite-Hadamard type inequalities by using our new notion of (s,r)−convex function via Riemann-Lioville fractional integrals.

Home automation is one of the fields working on automating home or household activities. The core objectives of the domotics technology are to save time and effort. Home automation can be implemented in various ways to achieve desire results. Currently, no home automation system can track the location of the person to perform some task at a particular time. We can make home automation more effective and efficient if we can implement a combination of techniques. This research aims to design and implement a hybrid technique based on the Global Position System and hand gestures in the field of home automation. Global Position System works when a person is outside the home, and the hand gesture technique is implemented when a person is present at home. By implementing a hybrid technique, we can overcome the limitations of the Global Position System and hand gesture technique. It is designed to replace sensors used in home automation system with another state-of-the-art technology, the Global Position System. Global Position System is a satellite-based technology that provides location and time information in all weather, anywhere on or near the Earth and hand gestures are used for making it intelligent by setting the trend. Idea is to integrate these two technologies and develop an automatic home automation system using Cellular Global Position System and moves a step forward in the field of automation. This research is useful for the disabled and elderly people for convenience, energy efficiency, and safety benefits and the general population as well.

In this paper, the classical notions of m-convex and m-concave sets are characterized under soft set environment and their important aggregation operations are discussed. Moreover, certain classical approaches (i.e. first and second senses) are employed on m-convex and m-concave soft sets to get more generalized results for uncertain scenarios.