Hermite-Hadamard type inequalities for (p1,h1)-(p2,h2)-convex functions on the co-ordinates

Yang, Wengui

doi:10.5556/j.tkjm.47.2016.1958

Cited by 10 publications

(4 citation statements)

References 25 publications

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“…Initially, Awan et al introduced the notion of (h 1 , h 2 )-convex functions and developed the following results [20]. Later, diferent authors used the notion of (h 1 , h 2 )-convexity and developed the following inequalities using related classes of convexity see references [21][22][23]. Te results developed using partial order relations, including inclusion relations, pseudoorder relations, and fuzzy order relations are not as accurate as the results developed using the center-radius method.…”

Section: Introductionmentioning

confidence: 99%

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Some Novel Estimates of Integral Inequalities for a Generalized Class of Harmonical Convex Mappings by Means of Center-Radius Order Relation

Afzal

Shabbir

Arshad

et al. 2023

Journal of Mathematics

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In interval analysis, integral inequalities are determined based on different types of order relations, including pseudo, fuzzy, inclusion, and various other partial order relations. By developing a link between center-radius (CR) order relations, it seeks to develop a theory of inequalities with novel estimates. A (CR)-order relation relationship differs from traditional interval-order relationships in that it is calculated as follows: q = q c , q r = q ¯ + q ¯ / 2 , q ¯ − q ¯ / 2 . There are several advantages to using this ordered relationship, including the fact that the inequality terms deduced from it yield much more precise results than any other partial-order relation defined in the literature. This study introduces the concept of harmonical h 1 , h 2 -convex functions associated with the center-radius order relations, which is very novel in literature. Applied to uncertainty, the center-radius order relation is an effective tool for studying inequalities. Our first step was to establish the Hermite−Hadamard H . H inequality and then to establish Jensen inequality using these notions. We discuss a few exceptional cases that could have practical applications. Moreover, examples are provided to verify the applicability of the theory developed in the present study.

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Section: Introductionmentioning

confidence: 99%

“…We get our research ideas from the extensive literature and specifc articles, see references [21,25]. Using the notions of harmonical convexity and center-radius order, we introduce a novel class of convexity called harmonical CR-(h 1 , h 2 )-convex functions.…”

Section: Introductionmentioning

confidence: 99%

Some Novel Estimates of Integral Inequalities for a Generalized Class of Harmonical Convex Mappings by Means of Center-Radius Order Relation

Afzal

Shabbir

Arshad

et al. 2023

Journal of Mathematics

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show abstract

“…Initially, the following authors developed the concept of (h 1 , h 2 )-convex functions and presented the following results [33]. There are various authors who use the concept of (h 1 , h 2 )-convexity to prove the following results for diverse classes of convexity, see [34][35][36][37]. Bai et al [38] and Afzal et al [39] use the concept of (h 1 , h 2 )-convexity to prove the following results for Hermite-Hadamard inequality and Jensen-type inequality.…”

Section: Introductionmentioning

confidence: 99%

Some Novel Estimates of Hermite–Hadamard and Jensen Type Inequalities for (h1,h2)-Convex Functions Pertaining to Total Order Relation

et al. 2022

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There are different types of order relations that are associated with interval analysis for determining integral inequalities. The purpose of this paper is to connect the inequalities terms to total order relations, often called (CR)-order. In contrast to classical interval-order relations, total order relations are quite different and novel in the literature and are calculated as ω=⟨ωc,ωr⟩=⟨ω¯+ω̲2,ω¯−ω̲2⟩. A major benefit of total order relations is that they produce more efficient results than other order relations. This study introduces the notion of CR-(h1,h2)-convex function using total order relations. Center and Radius order relations are a powerful tool for studying inequalities based on their properties and widespread application. Using this novel notion, we first developed some variants of Hermite–Hadamard inequality and then constructed Jensen inequality. Based on the results, this new concept is extremely useful in connection with a variety of inequalities. There are many new and well-known convex functions unified by this type of convexity. These results will stimulate further research on inequalities for fractional interval-valued functions and fuzzy interval-valued functions, as well as the optimization problems associated with them. For the purpose of verifying our main findings, we provide some nontrivial examples.

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“…In Ref. 9 some Hermite-Hadamard type inequalities for (p 1 , h 1 ) − (p 2 , h 2 )-convex functions on the coordinates were established. We now state some known results.…”

Section: Introductionmentioning

confidence: 99%

Some new Fejér type inequalities via quantum calculus on finite intervals

Yang¹

2017

ScienceAsia

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Hermite-Hadamard type inequalities for (p1,h1)-(p2,h2)-convex functions on the co-ordinates

Cited by 10 publications

References 25 publications

Some Novel Estimates of Integral Inequalities for a Generalized Class of Harmonical Convex Mappings by Means of Center-Radius Order Relation

Some Novel Estimates of Integral Inequalities for a Generalized Class of Harmonical Convex Mappings by Means of Center-Radius Order Relation

Some Novel Estimates of Hermite–Hadamard and Jensen Type Inequalities for (h1,h2)-Convex Functions Pertaining to Total Order Relation

Some new Fejér type inequalities via quantum calculus on finite intervals

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