Search

In this paper, we present generalized Jensen-Mercer inequality for a generalized h -convex function on fractal sets. We proved Hermite-Hadamard-Mercer local fractional integral inequalities via integral operators pertaining Mittag-Leffler kernel. Also, we drive two new local fractional integral identities for differentiable functions. By employing these integral identities, we derive some new Hermite-Mercer type inequalities for generalized h -convex function in local fractional calculus settings. Finally, we give some examples to emphasize the applications of derived results. These results will be a significant addition to Jensen-type inequalities in the literature. [ABSTRACT FROM AUTHOR]

This paper aims to investigate the notion of p -convex functions on fractal sets ℝ α ̂ (0 < α ̂ ≤ 1). Based on these novel ideas, we derived an auxiliary result depend on a three-step quadratic kernel by employing generalized p -convexity. Take into account the local fractal identity, we established novel Newton's type variants for the local differentiable functions. Several special cases are apprehended in the light of generalized convex functions and generalized harmonically convex functions. This novel strategy captures several existing results in the relative literature. Application is obtained in cumulative distribution function and generalized special weighted means to confirm the relevance and computational effectiveness of the considered method. Finally, we supposed that the consequences of this paper can stimulate those who are interested in fractal analysis. [ABSTRACT FROM AUTHOR]

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 ℝ α ̃ . By using our new approach, we established an auxiliary result that correlates with generalized convex () and concave functions for absolutely continuous functions with second-order local differentiable mappings. Moreover, we derived some companions of Ostrowski-type inequalities belonging to (2 α ̃) ∈ L ∞ [ s 1 , s 2 ] , (2 α ̃) ∈ L p [ s 1 , s 2 ] and (2 α ̃) ∈ L 1 [ s 1 , s 2 ] in local fractional sense. Our results generalize and offer better bounds than many known results in the existing literature associated with trapezoidal and midpoint formula. As an application perspective, we derived several estimation-type outcomes by the use of generalized α ̃ -type special means formula provided here to illustrate the usability of the obtained results. Our study contributes to a better understanding of fractal analysis and proves beneficial in exploring real-world phenomena. [ABSTRACT FROM AUTHOR]

The visual beauty reflects the practicability and superiority of design dependent on the fractal theory. Based on the applicability in practice, it shows that it is the completely feasible, self-comparability and multifaceted nature of fractal sets that made it an appealing field of research. There is a strong correlation between fractal sets and convexity due to its intriguing nature in the mathematical sciences. This paper investigates the notions of generalized exponentially harmonically (G E H ) convex and G E H s-convex functions on a real linear fractal sets R α (0 < α ≤ 1 ). Based on these novel ideas, we derive the generalized Hermite–Hadamard inequality, generalized Fejér–Hermite–Hadamard type inequality and Pachpatte type inequalities for G E H s-convex functions. Taking into account the local fractal identity; we establish a certain generalized Hermite–Hadamard type inequalities for local differentiable G E H s-convex functions. Meanwhile, another auxiliary result is employed to obtain the generalized Ostrowski type inequalities for the proposed techniques. Several special cases of the proposed concept are presented in the light of generalized exponentially harmonically convex, generalized harmonically convex and generalized harmonically s-convex. Meanwhile, an illustrative example and some novel applications in generalized special means are obtained to ensure the correctness of the present results. This novel strategy captures several existing results in the corresponding literature. Finally, we suppose that the consequences of this paper can stimulate those who are interested in fractal analysis. [ABSTRACT FROM AUTHOR]

Fractal analysis is one of interesting research areas of computer science and engineering, which depicts a precise description of phenomena in modeling. Visual beauty and self-similarity has made it an attractive field of research. The fractal sets are the effective tools to describe the accuracy of the inequalities for convex functions. In this paper, we employ linear fractals R α to investigate the (s , m) -convexity and relate them to derive generalized Hermite–Hadamard (HH) type inequalities and several other associated variants depending on an auxiliary result. Under this novel approach, we aim at establishing an analog with the help of local fractional integration. Meanwhile, we establish generalized Simpson-type inequalities for (s , m) -convex functions. The results in the frame of local fractional showed that among all comparisons, we can only see the correlation between novel strategies and the earlier consequences in generalized s-convex, generalized m-convex, and generalized convex functions. We obtain application in probability density functions and generalized special means to confirm the relevance and computational effectiveness of the considered method. Similar results in this dynamic field can also be widely applied to other types of fractals and explored similarly to what has been done in this paper. [ABSTRACT FROM AUTHOR]

In this paper, we introduce the α -type concept of generalized h -convex function on real linear fractal sets ℝ α   (0 < α ≤ 1) , from which the known definitions of generalized convex functions and generalized s -convex functions are derived, and from this, we obtain generalized Godunova–Levin functions and generalized P -functions. Some properties of generalized h -convex functions are discussed. Lastly, some generalized Hadamard-type inequalities of these classes functions are given. [ABSTRACT FROM AUTHOR]

In this paper, some new Jensen and Hermite-Hadamard inequalities for h-convex functions on fractal sets are obtained. Results proved in this paper may stimulate further research in this area. [ABSTRACT FROM AUTHOR]

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. [ABSTRACT FROM AUTHOR]