Fixed Point Theory

Convergence of the Mann and Ishikawa type iterations.

Results on the equivalence of the convergence of certain iterations have been obtained.

Local convergence of the successive approximations.

The high convergence orders of the successive approximations were characterized, an estimation of the attraction balls were obtained, and some results on the acceleration of the convergence of the successive approximations are given in:

Solutions of differential equations as fixed points.

In this direction we obtained existence, uniqueness results, data dependence and Ulam stability for the solution of functional-differential equations, differential equations with delays and mixed type argument.

The convergence of the sequence of the successive approximation by using contraction principle and step method with a weaker Lipschitz condition and a new algorithm of successive approximation sequence generated by the step method were obtained in