Some coincidence theorems and stability of iterative procedures

Singh, S. L.; Prasad, Bhagwati

doi:10.1016/j.camwa.2007.10.026

Cited by 80 publications

(48 citation statements)

References 9 publications

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“…We mention that the concept of (S,T)-stability was used in [26] and the transposition to (S,T)-weak stability in a metric space was introduced in [28].…”

Section: Definition 22 Let (X D) Be a Metric Space S T: X → X Bementioning

confidence: 99%

“…[26], assuming that lim n→∞ = 0, we should obtain that lim n→∞ = [28], we take an approximate sequence {S } of (S ). Then, there exists a decreasing sequence of nonnegative numbers { } converging to some ≥0, for n→∞, such that − ≤ , ≥ .…”

Section: We Will Show That the Picard Iteration Is Not (St)-stable mentioning

confidence: 99%

“…According to (S,T)-stability definition of [26], assuming that lim n→∞ = 0, we should obtain that lim n→∞ = For the (S,T)-weak stability, from the (S,T)-weak stability definition of [28], for any 0 ∈ 0,1 , the sequence { } generated by the iterative procedure +1 = , > 0,…”

Section: In Order To Study the (St)-weak Stability From The (St)-wmentioning

confidence: 99%

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On the Weak Stability of Picard Iteration for Some Contractive Type Mappings and Coincidence Theorems

Timiş¹

2012

IJCA

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Starting from a weak concept of stability, introduced by Berinde [1] and called "weak stability", in [27] we develop a weaker notion, named "w²-stability". Therefore, in this paper we prove some results of this weaker stability concept for certain class of mappings and also we give some examples of w²-stable but not weak stable nor stable iterations.Because of the restriction of an "approximate" sequence, some fixed point iteration procedures are not weakly stable so if it is used a weaker type of sequence, the stability can be obtained in the meaning of a new concept. General TermsFixed-point and coincidence theorems.

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“…We mention that the concept of (S,T)-stability was used in [26] and the transposition to (S,T)-weak stability in a metric space was introduced in [28].…”

Section: Definition 22 Let (X D) Be a Metric Space S T: X → X Bementioning

confidence: 99%

Section: We Will Show That the Picard Iteration Is Not (St)-stable mentioning

confidence: 99%

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On the Weak Stability of Picard Iteration for Some Contractive Type Mappings and Coincidence Theorems

Timiş¹

2012

IJCA

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“…Since then, several papers have been published on the fixed point theory of various classes of single-valued and multi-valued operators in b-metric spaces (see also [11,12,36]). Pacurar [32] proved some results on sequences of almost contractions and fixed points in b-metric spaces.…”

Section: Introductionmentioning

confidence: 99%

Existence of common fixed point for b-metric rational type contraction

Abbas

Cheema

Razani

2016

Filomat

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Abstract.The necessary conditions for existence of a common fixed point of two mappings satisfying generalized b-order contractive condition in the setting of a partially ordered b-complete b-metric space are presented. Also, we study well-posedness of common fixed point problem for generalized b-order contractive mappings. We employ our result to establish an existence of a solution of an integral equation.

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“…After the publication of this work, several coupled fixed point and coincidence point results have appeared in the recent literature. Works noted in ( [3,6,7,8,12,14,17,18,19])are some relevant examples. The aim of this article is to make further studies on such problems, and to generalize and complement some known results.…”

Section: Introductionmentioning

confidence: 99%