Ostrowski type fractional integral operators for generalized (;,,)−preinvex functions

In the present paper, the notion of generalized (;,,)−preinvex function is applied to establish some new generalizations of Ostrowski type inequalities via fractional integral operators. These results not only extend the results appeared in the literature but also provide new estimates on these type

Some new Hermite-Hadamard integral inequalities in multiplicative calculus

In this paper, we tend to establish some new Hermite–Hadamard type integral inequalities for multiplicatively convex function on coordinates and for product of two multiplicatively convex functions on coordinates.The National Natural Science Foundation of China.https://jaem.isikun.edu.tr/web/am2022Mathematics and Applied Mathematic

Some new inequalities for generalized convex functions pertaining generalized fractional integral operators and their applications

In this paper, authors establish a new identity for a differentiable function using generic integral operators. By applying it, some new integral inequalities of trapezium, Ostrowski and Simpson type are obtained. Moreover, several special cases have been studied in detail. Finally, many useful applications have been found.https://sciendo.com/journal/JAMSIam2022Mathematics and Applied Mathematic

Novel results on Hermite-Hadamard kind inequalities for η\eta-convex functions by means of (k,r)(k,r)-fractional integral operators

We establish new integral inequalities of Hermite-Hadamard type for the recent class of $\eta$-convex functions. This is done via generalized $(k,r)$-Riemann-Liouville fractional integral operators. Our results generalize some known theorems in the literature. By choosing different values for the parameters $k$ and $r$, one obtains interesting new results.Comment: This is a preprint of a paper whose final and definite form is a Springer chapter in the Book 'Advances in Mathematical Inequalities and Applications', published under the Birkhauser series 'Trends in Mathematics', ISSN: 2297-0215 [see http://www.springer.com/series/4961]. Submitted 02-Jan-2018; Revised 10-Jan-2018; Accepted 13-Feb-201

On Fejér type inequalities for convex mappings utilizing generalized fractional integrals

In this work, we first establish Hermite-Hadamard-Fejér type inequalities for convex function involving generalized fractional integrals with respect to another function which are generalization of some important fractional integrals such as the Riemann-Liouville fractional integrals and the Hadamard fractional integrals. Moreover, we obtain some trapezoid type inequalities for these kind of generalized fractional integrals. The results given in this paper provide generalization of several inequalities obtained in earlier studies

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

In this paper, the authors established several new inequalities of the Beesack–Wirtinger type for different kinds of differentiable convex functions. Furthermore, we generalized our results for functions that are n-times differentiable convex. Finally, many interesting Ostrowski- and Chebyshev-type inequalities are given as well

SOME NEW HERMITE-HADAMARD INTEGRAL INEQUALITIES IN MULTIPLICATIVE CALCULUS

In this paper, we tend to establish some new Hermite-Hadamard type integral inequalities for multiplicatively convex function on coordinates and for product of two multiplicatively convex functions on coordinates.National Natural Science Foundation of ChinaNational Natural Science Foundation of China (NSFC) [11971241]The first author is partially supported by the National Natural Science Foundation of China with the grant no: 11971241.WOS:0007044581000222-s2.0-8511919586

SOME NEW HERMITE-HADAMARD INTEGRAL INEQUALITIES IN MULTIPLICATIVE CALCULUS

In this paper, we tend to establish some new Hermite-Hadamard type integral inequalities for multiplicatively convex function on coordinates and for product of two multiplicatively convex functions on coordinates.National Natural Science Foundation of ChinaNational Natural Science Foundation of China (NSFC) [11971241]The first author is partially supported by the National Natural Science Foundation of China with the grant no: 11971241.WOS:0007044581000222-s2.0-8511919586