Stability of Jungck‐type iterative procedures

Abstract

We introduce and discuss the stability of Jungck and Jungck-Mann iterative procedures for a pair of Jungck-Osilike-type maps on an arbitrary set with values in a metric or linear metric space

Convergence and (S,T )- Stability Almost Surely for Random Jungck-Noor Type Iterative Scheme with Convergence Comparison

“…Singh et al [15] defined the following concept of ( S , T ) -stability: sequence generated by the iterative scheme Okeke and Kim [10] defined the stochastic verse of definition (2.4).…”

“…Jungck [8] in 1976, introduced the Jungck type iterative scheme and used it to find the common solution of two sequences satisfying contractive type conditions. Singh et al [15], gave the concept of Jungck-Mann iterative scheme and Olatinwo [13], generalized it by defining Jungck-Ishikawa and Jungck-Noor iterative schemes.In this direction Okeke and Kim [10] gave random fixed point results for Jangck-Mann type random iteration scheme and jungck-Ishikawa type iteration scheme. Rashwan et al [14] established some random fixed point results for Jungck-Noor type random iterative scheme.…”

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

“…Several other stability results exist in literature (for details see references [1] to [5], [7], [11], [12], [14] to [18]). …”

On the Stability and Strong Convergence for Jungck-Agarwal et al. Iteration Procedure

“…Some of them are the following: Then we have Picard iteration process which has been used to approximate the fixed point of mappings satisfying the inequality: [20,21], Osillike [16], Osilike and Udomene [15] ,Jachymski [8] ,Berinde [4,5] and Singh et al [24]. The summability theory of infinite matrices are used by Harder and Hicks [6], Rhoades [22], Osilike [23], and Singh et al [24] to prove different stability results for certain contractive conditions. The first stability result on T-stable mappings was due to Ostrowski [18] for the stability of Picard iteration using Banach contraction condition.…”