A local and semi-local convergence is developed of a class iterative methods without derivatives for solving nonlinear Banach space valued operator equations under the classical Lipschitz conditions first-order divided differences. Special cases this method are well-known algorithms, in particular, Secant, Kurchatov, Steffensen as well Newton method. For analysis, we use technique recurrent fun...

Dolores M. Cortez, Marc D. Feldman, Srinivas Mummidi, Anthony J. Valente, Bjorn Steffensen, Matthew Vincenti, Jeffrey L. Barnes, and Bysani Chandrasekar Department of Veterans Affairs South Texas Veterans Health Care System, and Departments of Medicine and Periodontics and Biochemistry, University of Texas Health Science Center, San Antonio, Texas; and Department of Medicine, Dartmouth Medical ...

In this paper, we present a weighted version of the Hermite–Hadamard inequality for convex functions on time scales, with weights that are allowed to take some negative values, these are the Steffensen–Popoviciu and the Hermite–Hadamard weights. We also present some applications of this inequality.