Abstract In this paper, we introduce notable Jensen–Mercer inequality for a general class of convex functions, namely uniformly functions. We explore some interesting properties such functions along with examples. As result, establish Hermite–Jensen–Mercer inequalities pertaining by considering the fractional integral operators. Moreover, Mercer–Ostrowski conformable operator via differentiable...

A mentor can mean the difference between a mentoree's failure and success. Yet mentoring is more than an altruistic venture. A good mentor will be more likely to recruit and retain strong student and postdoctoral candidates, and cultivate productive personnel. Despite these advantages, faculty often receive little, if any, mentoring training. Here, three panelists, Marianne Bronner-Fraser, Ph.D...

Many scholars have recently become interested in establishing integral inequalities using various known fractional operators. Fractional calculus has grown popularity as a result of its capacity to quickly solve real-world problems. First, we establish new the Hadamard–Mercer, Pachpatte–Mercer, and Dragomir–Agarwal–Mercer types containing an exponential kernel. In this regard, inequality proved...

We present a new method for density estimation based on Mercer kernels. The density estimate can be understood as the density induced on a data manifold by a mixture of Gaussians fit in a feature space. As is usual, the feature space and data manifold are defined with any suitable positive-definite kernel function. We modify the standard EM algorithm for mixtures of Gaussians to infer the param...

We characterize the reproducing kernel Hilbert spaces whose elements are p-integrable functions in terms of the boundedness of the integral operator whose kernel is the reproducing kernel. Moreover, for p = 2 we show that the spectral decomposition of this integral operator gives a complete description of the reproducing kernel.