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

Abstract

Abstract. In this paper, we introduce Jungck-Kirk-multistep and Jungck-Kirk-multistep-SP iterative schemes and use their strong convergences to approximate the common fixed point of nonself operators in a normed linear Space. The Jungck-KirkNoor, Jungck-Kirk-SP, Jungck-Kirk-Ishikawa, Jungck-Kirk-Mann and Jungck-Kirk iterative schemes follow our results as corollaries. We also study and prove stability results of these schemes in a normed linear space. Our results generalize and unify most approximation and stability results in the literature.

The equivalence between the (S,T)− stabilities of Jungck-type iterative schemes

“…In 2011 Olaleru J.O and Akewe H [10] prove that the convergence of these Jungck-iterations are equivalent. For more on the convergence of Jungck-type iterative scheme, the reader can consult [3,9]and the references therein.…”

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.…”