There are a number of results that provide bounds for integrals of products of functions. The main techniques that shall be employed in the current article involve the Steffensen inequality and a variety of bounds related to the Čebyšev functional. There have been some developments in both of these in the recent past with which the current author has been involved. These have been put to fruitf...

Abstract: In this paper, using the idea of Gander, families of several iterative methods for solving non-linear equations f (x) = 0 having zeros of higher multiplicity are presented. The families of methods presented here include methods of Newton type, Steffensen type and their variant. We obtain families of methods of order 2 as well as 3. Some numerical examples are also presented in support...

ABSTRACf The first complete proof of the criticality theorem for Bienayme-Galton-Watson branching processes was published in Danish in 1930 by J. F. Steffensen. In this report his paper is translated into English, together with another proof of the same result, obtained by C. M. Christensen at the same time. These papers are prefaced by a historical review by K. Albertsen on the problem of exti...

D.J. McKenzie, G. Piraccini, C. Agnisola, J.F. Steffensen, P. Bronzi, C.L. Bolis, B. Tota and E.W. Taylor School of Biological Sciences, University of Birmingham, Birmingham, (U.K.); Institute of Pharmacological Sciences, University of Milan, Milan (Italy); Department of General and Environmental Physiology, Federico II University of Naples, Naples (Italy); Helsingor Marine Laboratory, Universi...

Marion Korach-André, Paolo Parini, Lilian Larsson, Anders Arner, Knut R. Steffensen, and Jan-Åke Gustafsson Department of Biosciences and Nutrition at NOVUM, Karolinska Institutet; Division of Clinical Chemistry, Department of Laboratory Medicine, Karolinska Institutet at Karolinska University Hospital; Department of Physiology and Pharmacology, Karolinska Institutet, Huddinge, Sweden; and Cent...

We introduce the normalized Jensen-Mercer functional Mn( f ,x, p) = f (a)+ f (b)− n ∑ i=1 pi f (xi)− f ( a+b− n ∑ i=1 pixi ) and establish the inequalities of type MMn( f ,x,q) Mn( f ,x, p) mMn( f ,x,q) , where f is a convex function, x = (x1, . . . ,xn) and m and M are real numbers satisfying certain conditions. We prove them for the case when p and q are nonnegative n -tuples and when p and q...

In this paper, a family of Steffensen type methods of fourth-order convergence for solving nonlinear smooth equations is suggested. In the proposed methods, a linear combination of divided diferences is used to get a better approximation to the derivative of the given function. Each derivative-free member of the family requires only three evaluations of the given function per iteration. Therefo...

The dynamics of Steffesen-type methods, using a graphical tool for showing the basins of attraction, is presented. The study includes as particular cases, Steffesen-type modifications of the Newton, the two-steps, the Chebyshev, the Halley and the super– Halley iterative methods. The goal is to show that if we are interesting to preserve the convergence properties we must ensure that the deriva...