Hermite-Hadamard type integral inequalities for multidimensional general <i>h</i>-harmonic preinvex stochastic processes

Sharma, Nidhi; Mishra, Rohan; Hamdi, Abdelouahed

doi:10.1080/03610926.2020.1865403

Cited by 7 publications

(2 citation statements)

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“…Further, Ibrahim [10] introduced the concept of the strongly h-convex stochastic process. For more generalization of convex stochastic processes and related inequalities, see [11,15,23,24,25] and their references.…”

Section: Introductionmentioning

confidence: 99%

On Strongly m-Convex Stochastic Processes

Bisht,

Mishra,

Hamdi

2023

Preprint

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In this paper, we introduce the concept of strongly m-convex stochastic processes and present some basic properties of these stochastic processes. We derive the Hermite-Hadamard type inequalities for stochastic processes whose first derivatives in absolute values are strongly m-convex. The results presented in this paper are the generalization and extension of the previously known results. Mathematics Subject Classification (2010). 26A51, 26D15, 52A01, 60G99.

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Section: Introductionmentioning

confidence: 99%

On Strongly m-Convex Stochastic Processes

Bisht,

Mishra,

Hamdi

2023

Preprint

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“…Recently, Afzal et al [14] employed the notions of Riemann integral operator via center-radius order relations to develop a more generalized form of double inequality for harmonically CR-(h 1 , h 2 ) convex mappings. Sharma et al [15] developed Hermite-Hadamard inequalities based on general h-harmonic preinvex functions for real-valued stochastic processes. Based on exponentially (h, m)preinvexity, Chen et al [16] developed various variants of Hermite-Hadamard inequality based on Riemann-Liouville fractional integrals.…”

Section: Introductionmentioning

confidence: 99%

Some New Estimates of Hermite–Hadamard Inequalities for Harmonical cr-h-Convex Functions via Generalized Fractional Integral Operator on Set-Valued Mappings

Almalki,

Afzal

2023

Mathematics

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The application of fractional calculus to interval analysis is vital for the precise derivation of integral inequalities on set-valued mappings. The objective of this article is to reformulated the well-known Hermite–Hadamard inequality into various new variants via fractional integral operator (Riemann–Liouville ) and generalize the various previously published results on set-valued mappings via center and radius order relations using harmonical h-convex functions. First, using these notions, we developed the Hermite–Hadamard (H--H) inequality, and then constructed some product form of these inequalities for harmonically convex functions. Moreover, to demonstrate the correctness of these results, we constructed some interesting non-trivial examples.

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