Some New Beesack–Wirtinger-Type Inequalities Pertaining to Different Kinds of Convex Functions

In this paper, we shall discuss a newly introduced concept of center-radius total-ordered relations between two intervals. Here, we address the Hermite–Hadamard-, Fejér- and Pachpatte-type inequalities by considering interval-valued Riemann–Liouville fractional integrals. Interval-valued fractional inequalities for a new class of preinvexity, i.e., cr-h-preinvexity, are estimated. The fractional operator is used for the first time to prove such inequalities involving center–radius-ordered functions. Some numerical examples are also provided to validate the presented inequalities.

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Some Refinements of Hermite–Hadamard Type Integral Inequalities Involving Refined Convex Function of the Raina Type

Tariq

Sahoo²,

Ntouyas

2023

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The aim of this work is to elaborate and define the idea of refined convex function of the Raina type. In addition, we have attained some associated properties in the manner of the newly introduced idea. To add some more comprehension into the newly investigated definition, we obtain the estimations of the Hermite-Hadamard inequality. For the reader’s interest, we add some remarks regarding the Mittag-Leffer function. During the last four decades, the term Mitag-Leffler function has acquired popularity on account of its many importance in the fields of engineering and science, i.e statistical distribution theory, rheology, electric networks, fluid flow, and probability. The amazing perception regarding this function provides the solution of certain boundary value problems. The asymptotic status of this function plays a very vital performance in various problems of physics associated with fractional calculus. The methodology and amazing tools of this work may serve as an impetus for further research activities in this direction as well.

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Some New Beesack–Wirtinger-Type Inequalities Pertaining to Different Kinds of Convex Functions

Cited by 3 publications

References 32 publications

Inequalities for linear combinations of orthogonal projections and applications

Inequalities for linear combinations of orthogonal projections and applications

Modified Inequalities on Center-Radius Order Interval-Valued Functions Pertaining to Riemann–Liouville Fractional Integrals

Some Refinements of Hermite–Hadamard Type Integral Inequalities Involving Refined Convex Function of the Raina Type

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