The present article addresses the concept of p-convex functions on fractal sets. We are able to prove a novel auxiliary result. In the application aspect, the fidelity of the local fractional is used to establish the generalization of Simpson-type inequalities for the class of functions whose local fractional derivatives in absolute values at certain powers are p-convex. The method we present is an alternative in showing the classical variants associated with generalized p-convex functions. Some parts of our results cover the classical convex functions and classical harmonically convex functions. Some novel applications in random variables, cumulative distribution functions and generalized bivariate means are obtained to ensure the correctness of the present results. The present approach is efficient, reliable, and it can be used as an alternative to establishing new solutions for different types of fractals in computer graphics.

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Some new Simpson-type inequalities for generalized p -convex function on fractal sets with applications

The aim of this paper is to evaluate the potential improvement of classification results in the frame of discrete proportional fractional operator. The nonlocal kernel of the generalized proportional fractional sum depending on h -discrete exponential functions defined on time scale h Z . This paper deals novel discrete versions of the Polya-Szego and CebyseV type inequalities via discrete h -proportional fractional sums. These generalizations have potential utilities in the study of finite difference equations and statistical analysis. Taking into account the discrete h -proportional fractional sums, the main consequences concerns a quite general form of the Polya-Szego and CebyseV variants. In addition, the present investigation is a discrete analogue of integral inequalities established in the relative literature and also expands several discrete variants for nabla h -fractional sums in particular.

A unifying computational framework for novel estimates involving discrete fractional calculus approaches

The purpose of this paper is to provide novel estimates of Ostrowski-type inequalities in a much simpler and shorter way of some recent significant results in the context of a fractal set ℝα. By u...

New computations of ostrowski-type inequality pertaining to fractal style with applications

This paper aims to investigate the notion of p-convex functions on fractal sets ℝα(0 < α ≤ 1). Based on these novel ideas, we derived an auxiliary result depend on a three-step quadratic kernel b...

NEW NEWTON’S TYPE ESTIMATES PERTAINING TO LOCAL FRACTIONAL INTEGRAL VIA GENERALIZED p-CONVEXITY WITH APPLICATIONS

In this paper, some new fractal versions of Fejér–Hermite–Hadamard (FHH) type variants for generalized Raina [Formula: see text]-convex mappings are established benefiting from Raina’s function and fractal set [Formula: see text]. By means of three integral identities coupled with Raina’s function and local differentiation, we established some bounds for the difference between the left and central parts and also the difference between the center and right parts in FHH inequality. Besides that, some illustrative examples and noted special cases are apprehended. Additionally, we developed various generalizations for random variables, cumulative distribution functions, and special function theory as applications of local fractional integrals. The consequences established can provide contribution to inequality theory, fractional calculus and probability theory from the viewpoint of application to establish the other associated classes of functions. With the aid of these methodologies, it is promising to comprise further bounds of other type of variants which involve local fractional techniques. 

Revisiting Fejer-Hermite-Hadamard Type Inequalities in Fractal Domain and Applications

This article aims to investigate certain inequalities for generalized h-convexity on fractal sets R α , which are related to the famous Fejer–Hermite–Hadamard inequality. For this purpose, two identities for local differentiable mappings are established, based on which we provide certain estimates for the difference between the left and middle part as well as that of the middle and right part in the Fejer–Hermite–Hadamard inequality. Furthermore, we present five examples to illustrate the obtained results. As applications related to local fractional integrals, we construct several inequalities for random variables, cumulative distribution functions and numerical integrations.

Hao Wang

Papers

Fejér–Hermite–Hadamard type inequalities involving generalized h-convexity on fractal sets and their applications