Investigation of convergences and stabilities of some new fixed point iteration procedures

In this study, Jungck-multistep-SP iteration method, which is defined by Akewe [101], reduced to multistep-SP iteration method for S = I (identity operator). By using Kirk iteration [91] method we define some new iteration methods, which are called Kirkmultistep, Kirk-multistep-SP and Kirk-S iteration methods, as hybrid forms of multistep [93], multistep-SP and S-iteration [94] methods. It is shown that these iteration methods can be used to approximate to fixed points of contractive-like operators. Moreover, equivalence among convergences of multistep-SP iteration method, Siteration method [94] and some other well-known iteration methods for contractivelike operators were investigated. In addition, by utilizing the above-mentioned convergence results, some stability results for Kirk-multistep, Kirk-multistep-SP, Kirk-SP [100] and Kirk-S iteration methods were obtained. Finally, data dependence results of fixed points of contractive-like operators were investigated by employing multistep-SP and S-iteration [94] methods.