Strong convergence and stability of Kirk-multistep-type iterative schemes for contractive-type operators

Abstract

In this paper, we introduce Kirk-multistep and Kirk-multistep-SP iterative schemes and prove their strong convergences and stabilities for contractive-type operators in normed linear spaces. By taking numerical examples, we compare the convergence speed of our schemes (Kirk-multistep-SP iterative schemes) with the others (Kirk-SP, Kirk-Noor, Kirk-Ishikawa, Kirk-Mann and Kirk iterative schemes) for this class of operators. Our results generalize and extend most convergence and stability results in the literature. MSC: 47H09; 47H10

Random fixed point theorems in Banach spaces applied to a random nonlinear integral equation of the Hammerstein type

“…Furthermore, we apply our results in proving the existence of a solution of a nonlinear integral equation of the Hammerstein type. Our results unify, extend, and generalize several deterministic fixed point theorems in stochastic version, including the results of Akewe et al [4], Akewe and Okeke [3], Chugh et al [13], and Karahan and Ozdemir [21] among others.…”

On the Equivalence of Stochastic Fixed Point Iterations for Generalized φ-Contractive-Like Operators

“…The concept of employing various iterative schemes in approximating fixed points of contractive-like operators is very useful in fixed point theory and applications and other relevant fields like numerical analysis, operation research, and so forth (see [8][9][10][11][12][13][14][15]) This is due to the close relationship that exists between the problem of solving nonlinear equations and that of approximating fixed points of corresponding contractive-like operator.…”

Common fixed point of Jungck-Kirk-type iterations for non-self operators in normed linear spaces

“…In [2], Akewe, Okeke and Olayiwola introduced the Kirk-multistep and Kirk-multistep-SP iterative schemes and prove their strong convergences and stabilities for contractive-type operators in a normed linear space. In this work, we extend the map T used in [2] to a pair of maps S, T by introducing Jungck-Kirk-multistep and Jungck-Kirk-multistep-SP iterative schemes and use their convergences to approximate the common fixed points of a pair of nonself maps using contractive-type operators.…”

“…In this work, we extend the map T used in [2] to a pair of maps S, T by introducing Jungck-Kirk-multistep and Jungck-Kirk-multistep-SP iterative schemes and use their convergences to approximate the common fixed points of a pair of nonself maps using contractive-type operators. However, there are several iterative schemes in the literature for which the common fixed points of operators have been approximated over the years by various authors.The following schemes are some of them.…”