Iterations generated by tangential convex functions for solving equations

For solving nonlinear equations, Z. Szabó worked out the method based on always convergent iterations generated by tangential conic sections and some tangential convex functions. A recent paper generalising these iterations, a function family consisting of the basic iterating functions was built, whose members are obtained by the help of tangential convex functions, and which give always convergent methods. In this paper the properties and possibilities of application of these iterations are presented.