On Faster Implicit Hybrid Kirk-Multistep Schemes for Contractive-Type Operators

Abstract

The purpose of this paper is to prove strong convergence and T-stability results of some modified hybrid Kirk-Multistep iterations for contractive-type operator in normed linear spaces. Our results show through analytical and numerical approach that the modified hybrid schemes are better in terms of convergence rate than other hybrid Kirk-Multistep iterative schemes in the literature.

Continuous Dependence for Two Implicit Kirk-Type Algorithms in General Hyperbolic Spaces

“…We present the results for implicit Kirk-Mann and implicit Kirk-Ishikawa iterations using condition (3) and noting that both iterations converge strongly to a fixed point ∈ as proved in [12]. …”

“…Remarkable results have been investigated to date for more cases of Kirk-type schemes; see [8][9][10][11]. Recently in [12], the implicit Kirk-type schemes were introduced in Banach space for a contractive-type operator and it was also remarkable.…”

“…Hence, this paper aims to study closely the continuous contingency of two Kirk-type schemes in [12], namely, implicit Kirk-Mann and implicit Kirk-Ishikawa iterations in a general hyperbolic space. To do this, a certain approximate operator (say ) of is used to access the same source as in such a way that ( , ) ≤ for all ∈ and > 0.…”

Convergence Rate of Some Two-Step Iterative Schemes in Banach Spaces

“…Other iterations which have been studied also are Implicit Mann, Implicit Ishikawa, Thianwan, S-iteration, and hybrid Picard-Mann iterations. Recently, Wahab and Rauf [1] obtained some results on a faster implicit hybrid Kirk-multistep schemes for contractive type operators, to mention but a few.…”