Hermite-Hadamard Type Inequalities for Exponentially p-Convex Stochastic Processes

Özcan, Serap

doi:10.16984/saufenbilder.561040

Cited by 4 publications

(1 citation statement)

References 11 publications

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“…Also, inequalities akin to the above double inequality have been established for different classes of functions. See the following papers [4,6,7,9,10,[12][13][14] and their references for more. Not long ago, U.N. Katugampola [5] unified the aformentioned six integral operators as follows.…”

Section: Introductionmentioning

confidence: 99%

Generalized fractional inequalities of the Hermite-Hadamard type via new Katugampola generalized fractional integrals

Omaba

2022

Carpathian Math. Publ.

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A new generalization of the Katugampola generalized fractional integrals in terms of the Mittag-Leffler functions is proposed. Consequently, new generalizations of the Hermite-Hadamard inequalities by this newly proposed fractional integral operator, for a positive convex stochastic process, are established. Other known results are easily deduced as particular cases of these inequalities. The obtained results also hold for any convex function.

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Section: Introductionmentioning

confidence: 99%

Generalized fractional inequalities of the Hermite-Hadamard type via new Katugampola generalized fractional integrals

Omaba

2022

Carpathian Math. Publ.

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On strongly generalized convex stochastic processes

Sharma

Mishra

Hamdi

2022

Communications in Statistics - Theory and Methods

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New stochastic fractional integral and related inequalities of Jensen–Mercer and Hermite–Hadamard–Mercer type for convex stochastic processes

et al. 2023

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In this investigation, we unfold the Jensen–Mercer ($\mathtt{J-M}$ J − M ) inequality for convex stochastic processes via a new fractional integral operator. The incorporation of convex stochastic processes, the $\mathtt{J-M}$ J − M inequality and a fractional integral operator having an exponential kernel brings a new direction to the theory of inequalities. With this in mind, estimations of Hermite–Hadamard–Mercer ($\mathtt{H-H-M}$ H − H − M )-type fractional inequalities involving convex stochastic processes are presented. In the context of the new fractional integral operator, we also investigate a novel identity for differentiable mappings. Then, a new related $\mathtt{H-H-M}$ H − H − M -type inequality is presented using this identity as an auxiliary result. Applications to special means and matrices are also presented. These findings are particularly appealing from the perspective of optimization, as they provide a larger context to analyze optimization and mathematical programming problems.

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Hermite-Hadamard Type Inequalities for Exponentially p-Convex Stochastic Processes

Cited by 4 publications

References 11 publications

Generalized fractional inequalities of the Hermite-Hadamard type via new Katugampola generalized fractional integrals

Generalized fractional inequalities of the Hermite-Hadamard type via new Katugampola generalized fractional integrals

On strongly generalized convex stochastic processes

New stochastic fractional integral and related inequalities of Jensen–Mercer and Hermite–Hadamard–Mercer type for convex stochastic processes

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