Petrović-Type Inequalities for Harmonic <mml:math xmlns:mml="http://www.w3.org/1998/Math/MathML" id="M1"><mml:mi>h</mml:mi></mml:math>-convex Functions

Baloch, Imran Abbas; Chu, Yu‐Ming

doi:10.1155/2020/3075390

Cited by 25 publications

(3 citation statements)

References 64 publications

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“…Since that moment, a large number of researchers have put the concepts of fractional calculus to widespread use. As a result, they have obtained various novel and cutting-edge improvements of inequalities by using convexity and its extensions (see [17][18][19][20][21][22][23]).…”

Section: Introductionmentioning

confidence: 99%

Improvement in Some Inequalities via Jensen–Mercer Inequality and Fractional Extended Riemann–Liouville Integrals

Hyder,

Almoneef,

Budak

2023

Axioms

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The primary intent of this study is to establish some important inequalities of the Hermite–Hadamard, trapezoid, and midpoint types under fractional extended Riemann–Liouville integrals (FERLIs). The proofs are constructed using the renowned Jensen–Mercer, power-mean, and Holder inequalities. Various equalities for the FERLIs and convex functions are construed to be the mainstay for finding new results. Some connections between our main findings and previous research on Riemann–Liouville fractional integrals and FERLIs are also discussed. Moreover, a number of examples are featured, with graphical representations to illustrate and validate the accuracy of the new findings.

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Section: Introductionmentioning

confidence: 99%

Improvement in Some Inequalities via Jensen–Mercer Inequality and Fractional Extended Riemann–Liouville Integrals

Hyder,

Almoneef,

Budak

2023

Axioms

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“…Numerous mathematicians have generalized this inequality in numerous ways. For more related results, see [29][30][31][32][33][34][35][36][37][38][39][40][41][42][43][44]. The inequality is written as if T : I → R is a convex function on I and ı,  ∈ I with ı ≤  such that: (1)…”

Section: Introductionmentioning

confidence: 99%

New Versions of Fuzzy-Valued Integral Inclusion over p-Convex Fuzzy Number-Valued Mappings and Related Fuzzy Aumman’s Integral Inequalities

Alreshidi,

Khan,

Breaz

et al. 2023

Symmetry

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It is well known that both concepts of symmetry and convexity are directly connected. Similarly, in fuzzy theory, both ideas behave alike. It is important to note that real and interval-valued mappings are exceptional cases of fuzzy number-valued mappings (FNVMs) because fuzzy theory depends upon the unit interval that make a significant contribution to overcoming the issues that arise in the theory of interval analysis and fuzzy number theory. In this paper, the new class of p-convexity over up and down (UD) fuzzy relation has been introduced which is known as UD-p-convex fuzzy number-valued mappings (UD-p-convex FNVMs). We offer a thorough analysis of Hermite–Hadamard-type inequalities for FNVMs that are UD-p-convex using the fuzzy Aumann integral. Some previous results from the literature are expanded upon and broadly applied in our study. Additionally, we offer precise justifications for the key theorems that Kunt and İşcan first deduced in their article titled “Hermite–Hadamard–Fejer type inequalities for p-convex functions”. Some new and classical exceptional cases are also discussed. Finally, we illustrate our findings with well-defined examples.

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“…Thus, convex analysis and inequalities have been referred to as an absorbing field for the mathematicians due their wide applications in different branches of sciences. The reader can refer to [3][4][5][6][7][8]. Recently, Toplu et al [9], investigated a generalized form of convexity called n-polynomial convex function and obtained a corresponding H-H inequality.…”

Section: Introductionmentioning

confidence: 99%

Some New Mathematical Integral Inequalities Pertaining to Generalized Harmonic Convexity with Applications

et al. 2022

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The subject of convex analysis and integral inequalities represents a comprehensive and absorbing field of research within the field of mathematical interpretation. In recent times, the strategies of convex theory and integral inequalities have become the subject of intensive research at historical and contemporary times because of their applications in various branches of sciences. In this work, we reveal the idea of a new version of generalized harmonic convexity i.e., an m–polynomial p–harmonic s–type convex function. We discuss this new idea by employing some examples and demonstrating some interesting algebraic properties. Furthermore, this work leads us to establish some new generalized Hermite–Hadamard- and generalized Ostrowski-type integral identities. Additionally, employing Hölder’s inequality and the power-mean inequality, we present some refinements of the H–H (Hermite–Hadamard) inequality and Ostrowski inequalities. Finally, we investigate some applications to special means involving the established results. These new results yield us some generalizations of the prior results in the literature. We believe that the methodology and concept examined in this paper will further inspire interested researchers.

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Petrović-Type Inequalities for Harmonic h-convex Functions

Cited by 25 publications

References 64 publications

Improvement in Some Inequalities via Jensen–Mercer Inequality and Fractional Extended Riemann–Liouville Integrals

Improvement in Some Inequalities via Jensen–Mercer Inequality and Fractional Extended Riemann–Liouville Integrals

New Versions of Fuzzy-Valued Integral Inclusion over p-Convex Fuzzy Number-Valued Mappings and Related Fuzzy Aumman’s Integral Inequalities

Some New Mathematical Integral Inequalities Pertaining to Generalized Harmonic Convexity with Applications

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