In the present paper, we use the technique of differential subordination and superordination involving meromorphic functions with respect to symmetric points and also derive some sandwich results. As a consequence of main result, we obtain results for meromorphic starlike functions with respect to symmetrical points.

In this paper, we introduce a four step iterative algorithm which converges faster than some leading iterative algorithms in the literature. We show that our new iterative scheme is \(T\)-stable and data dependent. As an application, we use the new iterative algorithm to find the unique solution of a nonlinear integral equation. Our results are generalizations and improvements of several well known results in the existing literature.

The Simpson’s inequality cannot be applied to a function that is twice differentiable but not four times differentiable or have a bounded fourth derivative in the interval under consideration. Loads of articles are bound for twice differentiable convex functions but nothing, to the best of our knowledge, is known yet for twice differentiable exponentially convex and quasi-convex functions. In this paper, we aim to do justice to this query. For this, we prove several Simpson’s type inequalities for exponentially convex and exponentially quasi-convex functions. Our findings refine, generalize and complement existing results in the literature. We regain previously known results by taking \(\alpha=0\). In addition, we also show the importance of our results by applying them to some special means of positive real numbers and to the Simpson’s quadrature rule. The obtained results can be extended for different kinds of convex functions.

In this article, we consider the limit cycles of a class of planar polynomial differential systems of the form
$$\dot{x}=-y+\varepsilon (1+\sin ^{n}\theta )xP(x,y)$$
$$ \dot{y}=x+\varepsilon (1+\cos ^{m}\theta )yQ(x,y),
$$
where \(P(x,y)\) and \(Q(x,y)\) are polynomials of degree \(n_{1}\) and \(n_{2}\) respectively and \(\varepsilon\) is a small parameter. We obtain the maximum number of limit cycles that bifurcate from the periodic orbits of a linear center \(\dot{x}=-y, \dot{y}=x,\) by using the averaging theory of first order.

We show that a well-known asymptotic series for the logarithm of the central binomial coefficient is strictly enveloping in the sense of Pólya and Szegö, so the error incurred in truncating the series is of the same sign as the next term, and is bounded in magnitude by that term. We consider closely related asymptotic series for Binet’s function, for \(\ln\Gamma(z+\frac12)\), and for the Riemann-Siegel theta function, and make some historical remarks.

The aim of this paper is to study the tail distribution of the CEV model driven by Brownian motion and fractional Brownian motion. Based on the techniques of Malliavin calculus and a result established recently in [1], we obtain an explicit estimate for tail distributions.

In this paper, we prove some new formulas in the enumeration of labelled \(t\)-ary trees by path lengths. We treat trees having their edges oriented from a vertex of lower label towards a vertex of higher label. Among other results, we obtain counting formulas for the number of \(t\)-ary trees on \(n\) vertices in which there are paths of length \(\ell\) starting at a root with label \(i\) and ending at a vertex, sink, leaf sink, first child, non-first child and non-leaf. For each statistic, the average number of these reachable vertices is obtained for any random \(t\)-ary tree.

Medicinal plant’s quality and safety are becoming a great interest topic worldwide, especially due to contamination with heavy metals. The main objective of this study is to determine the phytochemical composition and quantify the concentration of heavy metals, trace and macro elements in fourteen medicinal plants purchased in the Central Market of San Salvador. Samples were dried and fractionated, subsequently digested and analyzed at first by phytochemical screening and then by atomic absorption spectrometry. The concentration of twelve elements was determined, only Matricaria chamomilla exceeded the established World Health Organization limit for Cd and Cu. Acourtia nudicaulis and Turnera diffusa exceeded the permitted concentration of Ni. The concentration of these elements must be inspected in medicinal plants sold in the informal markets of El Salvador to ensure the safety and quality. To our knowledge, this is the first study of heavy metals in medicinal plants conducted in El Salvador.

Due to the beneficial effects of anthocyanins on plants, animals and human beings, they have become the most interesting topic of research for scientists. They are being used in food industry as well as in pharmaceutical and cosmetic industries. Anthocyanins are present in red, blue, orange, purple, violet and intermediate color mostly. They are non-hazardous natural pigments that have positive impact on human health. They occur in nature since the evolution of flowering plants on earth. As humans were wild in ancient times, they consumed their large concentration through their diet and human digestive system is very active for their digestion. In this review, the chemistry and impact of anthocyanins on human health is discussed briefly.

This work deals with a boundary value problem for a nonlinear semipositone multi-point fractional differential equation. By using the Schauder fixed point theorem, we show the existence of one solution for this problem. Our result extend some recent works in the literature.