Approximate fixed point theorems of cyclical contraction mapping

Mohsenialhosseini, S. A. M.

doi:10.5937/matmor1701125m

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2020

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“…Lemma 2.7. [16] Let {X i } m i=1 be nonempty subsets of a metric space X and T : ∪ m i=1 X i → ∪ m i=1 X i be a cyclical operator. Let x 0 ∈ ∪ m i=1 X i and ε > 0.…”

Section: Preliminariesmentioning

confidence: 99%

Approximate fixed point theorems of cyclical contraction mapping on G-metric spaces

Mohsenialhosseini¹

2020

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In this paper, we will first introduce a new class of operators and contraction mapping for a cyclical map T on Gmetric spaces and the approximate fixed point property. Also, we prove two general lemmas regarding approximate fixed Point of cyclical contraction mapping on G-metric spaces. Using these results we prove several approximate fixed point theorems for a new class of operators such as Chatterjeat, Zamfirescu, Mohseni, Mohsenialhosseini on G-metric spaces (not necessarily complete). These results can be exploited to establish new approximate fixed point theorems for cyclical contraction maps on G-metric space. In addition, there is a new class of cyclical operators and contraction mapping on G-metric space (not necessarily complete) which do not need to be continuous. Finally, examples are given to support the usability of our results.

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“…Lemma 2.7. [16] Let {X i } m i=1 be nonempty subsets of a metric space X and T : ∪ m i=1 X i → ∪ m i=1 X i be a cyclical operator. Let x 0 ∈ ∪ m i=1 X i and ε > 0.…”

Section: Preliminariesmentioning

confidence: 99%