Some Hermite-Jensen-Mercer like inequalities for convex functions through a certain generalized fractional integrals and related results (original) (raw)
Some New Jensen–Mercer Type Integral Inequalities via Fractional Operators
Axioms
In this study, we present new variants of the Hermite–Hadamard inequality via non-conformable fractional integrals. These inequalities are proven for convex functions and differentiable functions whose derivatives in absolute value are generally convex. Our main results are established using the classical Jensen–Mercer inequality and its variants for (h,m)-convex modified functions proven in this paper. In addition to showing that our results support previously known results from the literature, we provide examples of their application.
Journal of Mathematics
In this paper, certain Hermite–Hadamard–Mercer-type inequalities are proved via Riemann–-Liouville fractional integral operators. We established several new variants of Hermite–Hadamard’s inequalities for Riemann–Liouville fractional integral operators by utilizing Jensen–Mercer inequality for differentiable mapping ϒ whose derivatives in the absolute values are convex. Moreover, we construct new lemmas for differentiable functions ϒ′, ϒ″, and ϒ‴ and formulate related inequalities for these differentiable functions using variants of Hölder’s inequality.
Certain Hermite–Hadamard type inequalities involving generalized fractional integral operators
Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-matematicas, 2017
Hermite-Hadamard inequality for convex functions via Riemann-Liouville fractional integrals. Here, motivated by the above-mentioned works, we aim at establishing extension and refinement of the Hermite-Hadamard type inequalities for a function with certain conditions by using new fractional integral operators introduced by Raina and Agarwal et al. above. The inequalities presented here are also pointed out to include some known results, as their special cases.
Generalized Hermite-Hadamard type inequalities involving fractional integral operators
Journal of Inequalities and Applications, 2017
In this article, a new general integral identity involving generalized fractional integral operators is established. With the help of this identity new Hermite-Hadamard type inequalities are obtained for functions whose absolute values of derivatives are convex. As a consequence, the main results of this paper generalize the existing Hermite-Hadamard type inequalities involving the Riemann-Liouville fractional integral.
Journal of Function Spaces, 2022
In this manuscript, we are getting some novel inequalities for convex functions by a new generalized fractional integral operator setting. Our results are established by merging the k , s -Riemann-Liouville fractional integral operator with the generalized Katugampola fractional integral operator. Certain special instances of our main results are considered. The detailed results extend and generalize some of the present results by applying some special values to the parameters.
Some Novel Fractional Integral Inequalities over a New Class of Generalized Convex Function
Fractal and Fractional
The comprehension of inequalities in convexity is very important for fractional calculus and its effectiveness in many applied sciences. In this article, we handle a novel investigation that depends on the Hermite–Hadamard-type inequalities concerning a monotonic increasing function. The proposed methodology deals with a new class of convexity and related integral and fractional inequalities. There exists a solid connection between fractional operators and convexity because of its fascinating nature in the numerical sciences. Some special cases have also been discussed, and several already-known inequalities have been recaptured to behave well. Some applications related to special means, q-digamma, modified Bessel functions, and matrices are discussed as well. The aftereffects of the plan show that the methodology can be applied directly and is computationally easy to understand and exact. We believe our findings generalise some well-known results in the literature on s-convexity.