Abstract
The most notable inequality pertaining convex functions is Jensen's inequality which has tremendous applications in several fields. Mercer introduced an important variant of Jensen's inequality called as Jensen-Mercer's inequality. Fractal sets are useful tools for describing the accuracy of inequalities in convex functions. The purpose of this paper is to establish a generalized Jensen-Mercer inequality for a generalized convex function on a real linear fractal set Double-struck capital R alpha (0 < alpha <= 1). Further, we also demonstrate some generalized Jensen-Mercer-type inequalities by employing local fractional calculus. Lastly, some applications related to Jensen-Mercer inequality and alpha-type special means are given. The present approach is efficient, reliable, and may motivate further research in this area.