In this work, the well-known Minkowski inequality is studied, using a generalized fractional integral operator, defined and studied by authors in a previous work. Relationships with known results are established throughout the work and in conclusions

La alerta por la pandemia causada por el coronavirus SARS-CoV-2 ha desatado una carrera contra el tiempo por búsqueda de un posible tratamiento. Varios fármacos antivirales empleados para controlar el desarrollo de la enfermedad, son derivados de moléculas obtenidas de plantas, sin embargo, su aislamiento puede resultar en la disminución o anulación del efecto. El uso de plantas ancestrales en países en vías de desarrollo, donde el acceso a un tratamiento farmacológico específico aún es limitado, las terapias naturales representan la primera línea de defensa frente al virus. En el presente estudio, se analizaron varias investigaciones respecto a la actividad in vitro de plantas sudamericanas con potencial actividad antiviral, clasificadas por países (Argentina, Brasil, Bolivia, Chile, Colombia, Ecuador, Paraguay, Perú, Uruguay y Venezuela). La familia Asteraceae presentó el mayor porcentaje de uso para el tratamiento de enfermedades respiratorias con un 18 %. Se concluye que la biodiversidad de plantas sudamericanas puede ser aprovechada, por lo que se sugiere realizar un estudio in vitro sobre el virus SARS-CoV-2.

Mercury (Hg) contamination is a problem that currently affects not only the environment but also human health. Various types of commercial adsorbents have been proposed for its removal. Silver is a noble element that can chemically adsorb mercury, forming amalgams. However, its use as an adsorbent presents the following disadvantages: rapid surface saturation and high cost. These limitations can easily be overcome using silver nanoparticles (AgNPs). With a size of less than 100 nm, their reactivity, their high surface area, and a minimal amount of metallic precursor, they are ideal candidates for mercury removal. This study presents a compendium of the use of conventional mercury adsorbents and the use of AgNPs for their colorimetric detection and removal in different matrices, in both the aqueous and gas phases of Hg0 and Hg2+ .In addition, the number of patents available in each case is analyzed. AgNPs as colorimetric sensors allow for quick detection of mercury in-situ. Additionally, the adsorption systems formed with AgNPs, allow for the obtaining of stable and chemically inert complexes, facilitating their recycling. It is concluded that the use of AgNPs is particularly efficient for the detection and removal of mercury, presenting a removal percentage of over 90%. As a result of the patents analyzed, its use is perfectly applicable at an industrial level.

En el presente artículo se establecen ciertos resultados de importancia para el análisis matemático, específicamente relacionados con las derivadas conformables de orden fraccional, entre ellos se destacan: la regla de la cadena, el Teorema del valor medio de Cauchy y la Regla de L’Hopital. Se espera que estos resultados estimulen la investigación en esta ́area

En el presente trabajo se encuentran resultados concernientes a la desigualdad integral de Hermite-Hadamard, y otras relacionadas con esta, usando funciones η−convexas y el operador integral fraccional definido por R.K. Raina.

We have found some new Ostrowski-type inequalities for functions whose derivative module is relatively (m, h1, h2) – convex. From the main results some corollaries refereeing to relative convexity, relative P−convexity, relative m−convexity, relative s−convexity in the second sense and relative (s,m)−convexity are deduced. Also, some inequalities of Hermite[1]Hadamard type are obtained

We found some new Ostrowski-type inequalities for functions whose derivative module is relatively convex, also some others of the same type making use of relatively s−convex functions in the second sense. With these results we obtain generalizations of results found by M. Alomari et. al. using convex and s−convex in the second sense.

En este artículo se estudia el carácter oscilatorio de una ecuación diferencial generalizada de orden α con α ∈ (0, 1]. se botienen criterios generalizados tipo Kamenev que son extensiones de resultados conocidos de la literatura para el caso tanto entero como fraccionario

In this paper, we have established some generalized inequalities of Hermite–Hadamard–Fejér type for generalized integrals. The results obtained are applied for fractional integrals of various type and therefore contain some previous results reported in the literature

Using the notion of s-ϕ-convex functions as generalization of convex functions, we estimate the difference between the middle and right terms in Hermite- Hadamard-Fejer inequality for differentiable mappings.

In the present work we introduce the class of (s,m)-convex functions on the coordinates and some new Ostrowski-type inequalities are deduced for this kind of generalized convex functions. The results obtained have the absolute value of the second partial derivative with respect to the coordinates (∂ 2 f /∂r∂t) in the aforementioned class and bounded, as a necessary condition. This generalizes the results for convex functions of . Also, some corollary is presented.

In the present work the Hermite-Hadamard inequality is established in the setting of quantum calculus for a generalized class of convex functions depending on three parameters: a number in (0, 1] and two arbitrary real functions defined on [0, 1]. From the proven results, various inequalities of the same type are deduced for other types of generalized convex functions. Also, the definition of dominated convex functions respect to the generalized class of convex functions aforementioned is introduced, and some integral inequalities are established.

In this paper, a quantum trapezium-type inequality using a new class of function, the so called generalized ϕ-convex function, is presented. A new quantum trapezium-type inequality for the product of two generalized ϕ-convex functions is provided. The authors also prove an identity for twice q-differentiable functions using Raina's function. Utilizing the identity established, certain quantum estimated inequalities for the above class are developed. Various special cases have been studied. A brief conclusion is also given.

There is a strong connection between convexity and inequalities. So, techniques from each concept applies to the other due to the strong correlation between them; specifically, in the past few years. In this attempt, we consider the Hermite–Hadamard inequality and related inequalities for the class of functions whose absolute value of the third derivative are quasi-convex functions. Finally, the applications of our findings for special functions and particular functions are pointed out.

In this paper, the study is focused on the quantum estimates of Ostrowski type inequalities for q-differentiable functions involving the special function introduced by R.K. Raina which depends on certain parameters. Our methodology involves Jackson’s q-integral, the basic concepts of quantum calculus, and a generalization of a class of special functions used in the frame of convex sets and convex functions. As a main result, some quantum estimates for the aforementioned inequality are established and some cases involving the special hypergeometric and Mittag–Leffler functions have been studied and some known results are deduced.

In recent years, new classes of convex functions have been introduced in order to generalize the results and to obtain new estimations. In this paper, we give generalization of the Jensen’s inequality by using definition of convex functions on n–coordinates. Results given in [10] are particular cases of results given here.

La desigualdad integral de Jensen tiene mucha importancia en cuanto a sus aplicaciones en diferentes campos de las matemáticas. En este artículo encontramos una nueva desigualdad tipo Jensen para funciones cuya segunda derivada en valor absoluto es $varphi$-convexa.