40 research outputs found
Hermite-Hadamard Type Inequalities for Quasi-Convex Functions via Katugampola Fractional Integrals
The paper deals with quasi-convex functions, Katugampola fractional integrals and Hermite-Hadamard type integral inequalities. The main idea of this paper is to present new Hermite-Hadamard type inequalities for quasi-convex functions using Katugampola fractional integrals, Hölder inequality and the identities in the literature
An approximation formula for the Katugampola integral
The objective of this paper is to present an approximation formula
for the Katugampola fractional integral, that allows us to solve fractional
problems with dependence on this type of fractional operator. The formula
only depends on first-order derivatives, and thus converts the fractional problem
into a standard one. With some examples, we show the accuracy of the
method, and then we present the utility of the method by solving a fractional
integral equation
Jensen-type inequalities for m-convex functions
Inequalities play an important role in pure and applied mathematics. In particular, Jensen's inequality, one of the most famous inequalities, plays a main role in the study of the existence and uniqueness of initial and boundary value problems for differential equations. In this work we prove some new Jensen-type inequalities for m-convex functions, and apply them to generalized Riemann-Liouville-type integral operators. Furthermore, as a remarkable consequence, some new inequalities for convex functions are obtained.The research of Yamilet Quintana, José M. Rodríguez, and José M. Sigarreta is supported by a grant from Agencia Estatal de Investigación (PID2019-106433GB-I00/AEI/10.13039/501100011033), Spain. The research of Yamilet Quintana and José M. Rodríguez is supported by the Madrid Government (Comunidad de Madrid-Spain) under the Multiannual Agreement with UC3M in the line of Excellence of University Professors (EPUC3M23) and in the context of the V PRICIT (Regional Programme of Research and Technological Innovation)
Integral inequalities for s-convexity via generalized fractional integrals on fractal sets
In this study, we establish new integral inequalities of the Hermite–Hadamard type for s-convexity via the Katugampola fractional integral. This generalizes the Hadamard fractional integrals and Riemann–Liouville into a single form. We show that the new integral inequalities of Hermite–Hadamard type can be obtained via the Riemann–Liouville fractional integral. Finally, we give some applications to special means