A Study on the Modified Form of Riemann-Type Fractional Inequalities via Convex Functions and Related Applications

In this article, we provide constraints for the sum by employing a generalized modified form of fractional integrals of Riemann-type via convex functions. The mean fractional inequalities for functions with convex absolute value derivatives are discovered. Hermite–Hadamard-type fractional inequalities for a symmetric convex function are explored. These results are achieved using a fresh and innovative methodology for the modified form of generalized fractional integrals. Some applications for the results explored in the paper are briefly reviewed.The sixth author is grateful to the Spanish Government and the European Commission for its support through grant RTI2018-094336-B-I00 (MCIU/AEI/FEDER, UE) and to the Basque Government for its support through grants IT1207-19 and IT1555-22

New generalized midpoint type inequalities for fractional integral

Agarwal, Praveen/0000-0001-7556-8942WOS: 000504461100011Here, our first aim to establish a new identity for differentiable function involving Riemann-Liouville fractional integrals. Then, we obtain same generalized midpoint type inequalities utilizing convex and concave function

Integral Inequalities of Hermite-Hadamard Type Via Green Function and Applications

In this study, we establish some Hermite- Hadamard type inequalities for functions whose second derivatives absolute value are convex. In accordance with this purpose, we obtain an identity using Green\u27s function. Then using this equality we get our main results

POST-QUANTUM HERMITE-JENSEN-MERCER INEQUALITIES

The Jensen-Mercer inequality, which is well known in the literature, has an important place in mathematics and related disciplines. In this work, we obtain the Hermite-Jensen-Mercer inequality for post-quantum integrals by utilizing Jensen-Mercer inequalities. Then we investigate the connections between our results and those in earlier works. Moreover, we give some examples to illustrate our main results. This is the first paper about Hermite-Jensen-Mercer inequalities for post-quantum integrals

On Fejér Type Inequalities For Products Two Convex Functions

In this paper, we first obtain some new Fejér type inequalities for products of two convex mappings. Moreover, by applying these inequalities for Riemann-Liouville fractional integrals, we establish some Fejér type inequalities involving Riemann-Liouville fractional integrals. The most important feature of our work is that it contains Fejér type inequalities for both classical integrals and fractional integrals

Some New Hermite–Hadamard Type Inequalities Pertaining to Generalized Multiplicative Fractional Integrals

There is significant interaction between the class of symmetric functions and other types of functions. The multiplicative convex function class, which is intimately related to the idea of symmetry, is one of them. In this paper, we obtain some new generalized multiplicative fractional Hermite–Hadamard type inequalities for multiplicative convex functions and for their product. Additionally, we derive a number of inequalities for multiplicative convex functions related to generalized multiplicative fractional integrals utilising a novel identity as an auxiliary result. We provide some examples for the appropriate selections of multiplicative convex functions and their graphical representations to verify the authenticity of our main results.Basque Government: Grants IT1555-22 and KK-2022/00090; and MCIN/AEI 269.10.13039/501100011033 for Grant PID2021-1235430B-C21/C22

NEW TRAPEZOID TYPE INEQUALITIES FOR DIFFERENTIABLE FUNCTIONS

In this paper, we first establish that an identity involving generalized fractional integrals for twice differentiable functions. By using this equality, we obtain some trapezoid type inequalities for the functions whose second derivatives in absolute value are convex

Some fractional estimates of upper bounds involving functions having exponential convexity property

The main objective of this article is to consider the class of exponentially convex functions. We derive a new integral identity involving Riemann-Liouville fractional integral. Utilizing this identity as an auxiliary result we obtain new fractional bounds involving the functions having exponential convexity property.Publisher's Versio

Some properties of generalized (S, k)-bessel function in two variables

The devotion of this paper is to study the Bessel function of two variables in k-calculus. we discuss the generating function of k-Bessel function in two variables and develop its relations. After this we introduce the generalized (s, k)-Bessel function of two variables which help to develop its generating function. The s-analogy of k-Bessel function in two variables is also discussed. Some recurrence relations of the generalized (s, k)-Bessel function in two variables are also derived. © 2022 All rights reserved