Harmonic Convex Functions Research Articles

Relations of Harmonic Starlike Function Subclasses with Mittag–Leffler Function

In this study, the connection between certain subfamilies of harmonic univalent functions is established by utilizing a convolution operator involving the Mittag–Leffler function. The investigation reveals inclusion relations concerning harmonic γ-uniformly starlike mappings in the open unit disc, harmonic starlike functions and harmonic convex functions, highlighting the improvements given by the results presented here on previously published outcomes.

Hermite–Hadamard-type inequalities for multiplicative harmonic s -convex functions

UDC 517.5 We study the concept of multiplicative harmonic s -convex functions and establish Hermite–Hadamard integral inequalities for this class of functions. Furthermore, we derive a set of Hermite–Hadamard-type inequalities applicable to the product and quotient of multiplicative harmonic s -convex functions. In addition, we deduce new inequalities involving multiplicative integrals for the product and quotient of harmonic convex and multiplicative harmonic s -convex functions. Some results for the class of multiplicative harmonic convex functions are obtained as special cases of our results. The obtained results are verified by providing examples with included graphs.

New Auxiliary Principle Technique for General Harmonic Directional Variational Inequalities

This paper explores the utilisation of harmonic variational inequalities to establish the minimum value among two locally Lipschitz continuous harmonic convex functions. This investigation introduces novel classes of harmonic directed variational inequalities, particularly focusing on scenarios like harmonic complementarity and related optimization challenges. The study proposes and analyses various inertial iterative strategies for addressing harmonic directed variational inequalities through the auxiliary principle technique. It examines convergence criteria under specific weak conditions, emphasising the simplicity of the approach compared to other methodologies. The findings presented herein have broad applicability in the context of harmonic variational inequalities and optimization problems, though they are limited to theoretical exploration. Further research is required to implement these strategies numerically.

Hermite–Hadamard type inequalities for multiplicatively harmonic convex functions

In this work, the notion of a multiplicative harmonic convex function is examined, and Hermite–Hadamard inequalities for this class of functions are established. Many inequalities of Hermite–Hadamard type are also taken into account for the product and quotient of multiplicative harmonic convex functions. In addition, new multiplicative integral-based inequalities are found for the quotient and product of multiplicative harmonic convex and harmonic convex functions. In addition, we provide certain upper limits for such classes of functions. The obtained results have been verified by providing examples with included graphs. The findings of this study may encourage more research in several scientific areas.

Harmonic functions associated with Pascal distribution series

The primary objective of this paper is to explore the application of a specific convolution operator, which incorporates the Pascal distribution series. Through this investigation, we establish essential inclusion relations between the harmonic class HΥ(ϱ,ξ) and other classes of harmonic functions, namely, harmonic starlike functions and harmonic convex functions, all defined within the confines of the open unit disk. Moreover, we derive consequential outcomes from our main findings. The study delves into the intriguing interplay among these harmonic function classes, shedding light on their underlying properties and mutual connections. The presented results contribute to a deeper understanding of harmonic functions and provide a valuable basis for further research in this area.

Some New Classes of Harmonic Hemivariational Inequalities

Some new classes of harmonic hemivariational inequalities are introduced and investigated in this paper. It has been shown that the optimality conditions of the sum of two harmonic convex functions can be characterized by the harmonic hemivariational inequalities. Several special cases such as harmonic complementarity problems and related harmonic problems are discussed. The auxiliary principle technique is applied to suggest and analyze some iterative schemes for harmonic hemivariational inequalities. We prove the convergence of these iterative methods under some weak conditions. Our method of proof of the convergence criteria is simple compared to other techniques. Results obtained in this paper continue to hold for new and known classes of harmonic variational inequalities and related optimization problems. The ideas and techniques of this paper may inspire further research in various branches of pure and applied sciences.

On some inequalities of Fejér’s type using the notion of harmonic convexity

In this study, weintroduce some new mappings in connection with Hermite-Hadamard and Fej?r type integral inequalities which have been proved using the harmonic convex functions. As a consequence, we discover certain new inequalities of the Fej?r type that provide refinements of the Hermite-Hadamard and Fej?r type integral inequalities that have already been obtained.

HERMITE–HADAMARD-TYPE INEQUALITIES INVOLVING SEVERAL KINDS OF FRACTIONAL CALCULUS FOR HARMONICALLY CONVEX FUNCTIONS

In this paper, we use the properties of Atangana–Baleanu (AB) fractional calculus and Prabhakar fractional calculus to construct some novel Hermite–Hadamard-type fractional integral inequalities for harmonically convex functions. And these inequalities are represented by the Mittag-Leffler functions. Finally, several special inequalities are established to illustrate the applications of our conclusions in special means.

On harmonic convex functions of three variables and related Hermite-Hadamard inequalities

The main objective of this paper is to extend the notion of harmonic convex functions for three variables. Some associated Hermite-Hadamard type of integral inequalities are also obtained.

Mappings related to Hermite-Hadamard type inequalities for harmonically convex functions

In this study, we define some mappings connected to the Hermite-Hadamard type inequalities constructed for harmonically convex mappings. We investigate some properties of these mappings and provide some refinement inequalities for the Hermite-Hadamard type inequalities that have already been established for harmonic convex functions.

Weighted Integral Inequalities for Harmonic Convex Functions in Connection with Fejér’s Result

In this study, on the subject of harmonic convex functions, we introduce some new functionals linked with weighted integral inequalities for harmonic convex functions. In addition, certain new inequalities of the Fejér type are discovered.

Some Results of a Harmonic Family of Analytic Functions Connected with Poisson Distribution Series

This article aims to gain implicit relations among different subclasses of harmonic family of analytic functions containing with some description for Poisson distribution series to be in the new subclasses of harmonic convex functions and harmonic starlike, \U0001d4a6\U0001d4b2(α) and respectively, in the plane.

Some Generalized Fractional Integral Inequalities via Harmonic Convex Functions and Their Applications

The aim of this paper is to derive from an auxiliary identity some new generalizations of fractional integral inequalities of Simpson, midpoint, and trapezoid using the class of harmonic convex functions. To show that our results are quite unifying, we discuss several new special cases. Finally, some applications regarding error estimations for the Simpson quadrature formula are presented to support our theoretical results.

New fractional identities, associated novel fractional inequalities with applications to means and error estimations for quadrature formulas

In this paper, the authors derive some new generalizations of fractional trapezium-like inequalities using the class of harmonic convex functions. Moreover, three new fractional integral identities are given, and on using them as auxiliary results some interesting integral inequalities are found. Finally, in order to show the efficiency of our main results, some applications to special means for different positive real numbers and error estimations for quadrature formulas are obtained.

Hermite-Hadamard-Fejér type fractional inequalities relating to a convex harmonic function and a positive symmetric increasing function

<abstract><p>The purpose of this article is to discuss some midpoint type HHF fractional integral inequalities and related results for a class of fractional operators (weighted fractional operators) that refer to harmonic convex functions with respect to an increasing function that contains a positive weighted symmetric function with respect to the harmonic mean of the endpoints of the interval. It can be concluded from all derived inequalities that our study generalizes a large number of well-known inequalities involving both classical and Riemann-Liouville fractional integral inequalities.</p></abstract>

A Study of Uniform Harmonic χ -Convex Functions with respect to Hermite-Hadamard’s Inequality and Its Caputo-Fabrizio Fractional Analogue and Applications

In this paper, we introduce the notion of uniform harmonic χ -convex functions. We show that this class relates several other unrelated classes of uniform harmonic convex functions. We derive a new version of Hermite-Hadamard’s inequality and its fractional analogue. We also derive a new fractional integral identity using Caputo-Fabrizio fractional integrals. Utilizing this integral identity as an auxiliary result, we obtain new fractional Dragomir-Agarwal type of inequalities involving differentiable uniform harmonic χ -convex functions. We discuss numerous new special cases which show that our results are quite unifying. Finally, in order to show the significance of the main results, we discuss some applications to means of positive real numbers.

Properties and Bounds of Jensen-Type Functionals via Harmonic Convex Functions

Dragomir introduced the Jensen-type inequality for harmonic convex functions (HCF) and Baloch et al. studied its different variants, such as Jensen-type inequality for harmonic h -convex functions. In this paper, we aim to establish the functional form of inequalities presented by Baloch et al. and prove the superadditivity and monotonicity properties of these functionals. Furthermore, we derive the bound for these functionals under certain conditions. Furthermore, we define more generalized functionals involving monotonic nondecreasing concave function as well as evince superadditivity and monotonicity properties of these generalized functionals.

Some δ -Tempered Fractional Hermite–Hadamard Inequalities Involving Harmonically Convex Functions and Applications

The main objective of this paper is to obtain some new δ -tempered fractional versions of Hermite–Hadamard’s inequality using the class of harmonic convex functions. In order to show the significance of the main results, we also discuss some interesting applications.

Some Ostrowski type integral inequalities via generalized harmonic convex functions

In this paper, we aim to introduce a new notion of convex functions namely the harmonic \(s\)-type convex functions. The refinements of Ostrowski type inequality are investigated which are the generalized and extended variants of the previously known results for harmonic convex functions.

On Fejér sort inequalities for products two harmonically-convex functions via fractional integrals

In this paper, some new estimates on Fej?r sort inequalities via Riemann Liouville fractional integral for the products of two harmonically-convex functions are obtained.