Generalized fractal Jensen and Jensen–Mercer inequalities for harmonic convex function with applications

Abstract

In this paper, we present a generalized Jensen-type inequality for generalized harmonically convex function on the fractal sets, and a generalized Jensen–Mercer inequality involving local fractional integrals is obtained. Moreover, we establish some generalized Jensen–Mercer-type local fractional integral inequalities for harmonically convex function. Also, we obtain some generalized related results using these inequalities on the fractal space. Finally, we give applications of generalized means and probability density function.

Exponentially Convex Functions on the Coordinates and Novel Estimations via Riemann-Liouville Fractional Operator

“…In [19], Agarwal et al have proved many new inequalities of the Hadamard type by using the generalized k − fractional integral operator. Recently, several new integral inequalities of Jensen, Jensen-Mercer, and Hadamard type have been provided via generalized fractional integral operators in [20,21] and [22].…”

A generalized local fractional LWR model of vehicular traffic flow and its solution

“…In the modern era, many problems have been described using local fractional derivatives and integrals, including diffusion and heat equations involving local fractional operators [22], 2‐D Burgers‐type equations with local fractional derivatives [23], nonlinear local fractional Riccati differential equations [24] and local fractional Burgers equations [25], fractal nonlinear Burgers' equation [26], and Schamel's equation with local fractional derivative [27]. Recently, Razzaq et al use local fractional integral to analyze generalized F‐convex function with generalized Hermite‐Hadamard type inequalities [28] while generalized fractal Jensen and Jensen‐Mercer inequalities are examined by Butt et al for harmonic convex function [29]. Local fractional bidirectional propagation system of equations is examined by Sang et al [30].…”

Some integral inequalities via new generalized harmonically convexity

“…In order to estimate and improve the error bounds for some well‐known integral inequalities, including the trapezoidal, midpoint, and Ostrowski‐type inequalities, inequality () has been established and generalized in numerous ways for various classes of convex functions [3–28]. Dragomir and Agarwal [11] established some inequalities of the trapezoidal type for differentiable convex functions by taking into consideration the above inequality.…”