In this paper, we establish some conformable fractional Hermite-Hadamard type integral inequalities via harmonic s-convexity, and the estimates of the products of two harmonic s-convexfunctions are also considered.
In this paper, we establish some conformable fractional Hermite-Hadamard type integral inequalities via harmonic s-convexity, and the estimates of the products of two harmonic s-convexfunctions are also considered.
In this paper, we introduce a new class of convexfunctions, which is called generalized harmonic convex functions on fractal sets ℝα (0 α ≤ 1). This new class of convexfunctions includes generalized convex functi...
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In this paper, we derive a new extension of Hermite-Hadamard's inequality via k-Riemann-Liouville fractional integrals. Two new k-fractional integral identities are also derived. Then, using these identities as an...
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In this paper, we derive a new extension of Hermite-Hadamard's inequality via k-Riemann-Liouville fractional integrals. Two new k-fractional integral identities are also derived. Then, using these identities as an auxiliary result, we obtain some new k-fractional bounds which involve k-Appell's hypergeometric functions. These bounds can be viewed as new k-fractional estimations of trapezoidal and mid-point type inequalities. These results are obtained for the functions which have the harmonicconvexity property. We also discuss some special cases which can be deduced from the main results of the paper.
We establish new conformable fractional Hermite-Hadamard (H-H) Mercer type inequalities for harmonically convexfunctions using the concept of support line. We introduce two new conformable fractional auxiliary equali...
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We establish new conformable fractional Hermite-Hadamard (H-H) Mercer type inequalities for harmonically convexfunctions using the concept of support line. We introduce two new conformable fractional auxiliary equalities in the Mercer sense and apply them to differentiable functions with harmonicconvexity. We also use Power-mean, H & ouml;lder's and improved H & ouml;lder inequality to derive new Mercer type inequalities via conformable fractional integrals. The accuracy and superiority of the offered technique are clearly depicted through impactful visual illustrations. We also use our technique to derive new estimates for hypergeometric functions and special means of real numbers that are more precise than existing ones. Some applications are provided as well. Our results generalize and extend some existing ones in the literature.
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