In the presented paper, Levinson's inequality for the 3-convex function is generalized by using two Green functions.Čebyšev-, Grüss-and Ostrowski-type new bounds are found for the functionals involving data points of two types. Moreover, the main results are applied to information theory via the f -divergence, the Rényi divergence, the Rényi entropy, the Shannon entropy and the Zipf-Mandelbrot law.

The aim of this work is to present a new fractional order model of novel coronavirus (nCoV-2019) under Caputo-Fabrizio derivative. We make use of fixed point theory and Picard-Lindelöf technique to explore the existence and uniqueness of solution for the proposed model. Moreover, we explore the generalized Hyers-Ulam stability of the model using Gronwall's inequality.

In this paper, Levinson type inequalities are studied for the class of higher order convex functions by using Abel-Gontscharoff interpolation. Cebyšev, Grüss, and Ostrowski-type new bounds are also found for the functionals involving data points of two types.

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The purpose of this paper is to define a new contractive type mapping called Z ϑ-contraction and prove some fixed point and Suzuki type fixed point results in the context of complete metric spaces for such contraction and present some examples of the obtained results for illustration. Moreover, we present an application for the existence of a solution of certain nonlinear integral equations. INDEX TERMS Simulation functions, ϑ-contraction, integral equations.