Browsing by Author "Rodríguez, José M."
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Item Jensen-type inequalities for m-convex functions(2022) Bosch, Paul; Quintana, Yamilet; Rodríguez, José M.; Sigarreta, José M.Inequalities play an important role in pure and applied mathematics. In particular, Jensen’s inequality, one of the most famous inequalities, plays the 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-Liouvilletype integral operators. Furthermore, as a remarkable consequence, some new inequalities for convex functions are obtained.Item On Ostrowski Type Inequalities for Generalized Integral Operators(2022) Cruz, Martha Paola; Abreu-Blaya, Ricardo; Bosch, Paul; Rodríguez, José M.; Sigarreta, José M.It is well known that mathematical inequalities have played a very important role in solving both theoretical and practical problems. In this paper, we show some new results related to Ostrowski type inequalities for generalized integral operators.Publication Oscillation results for a nonlinear fractional differential equation(2023) Bosch, Paul; Rodríguez, José M.; Sigarreta, José M.In this paper, the authors work with a general formulation of the fractional derivative of Caputo type. They study oscillatory solutions of differential equations involving these general fractional derivatives. In particular, they extend the Kamenev-type oscillation criterion given by Baleanu et al. in 2015. In addition, we prove results on the existence and uniqueness of solutions for many of the equations considered. Also, they complete their study with some examples.Publication Some new Milne-type inequalities(2024) Bosch, Paul; Rodríguez, José M.; Sigarreta, José M.; Tourís, EvaInequalities play a main role in pure and applied mathematics. In this paper, we prove a generalization of Milne inequality for any measure space. The argument in the proof of this inequality allows us to obtain other Milne-type inequalities. Also, we improve the discrete version of Milne inequality, which holds for any positive value of the parameter p. Finally, we present a Milne-type inequality in the fractional context.