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Dergiler / Hacettepe Journal of Mathematics and Statistics / 2014 / Cilt: 43 - Sayı: 4

Edelstein-type fixed point theorems in compact TVS-cone metric spaces

Thabet ABDELJAWAD
Sayfa
561–569
Yayın Tarihi
2022-10-18
DOI
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Moreover, different versions of the two theorems are proved in TVS-cone metric spacesby making use of the nonlinear scalarization function used very recentlyby Wei-Shih Du in [A note on cone metric fixed point theory and itsequivalence, Nonlinear Analysis,72(5),2259-2261 (2010).] to prove theequivalence of the Banach contraction principle in cone metric spacesand usual metric spaces.

📌 3 Maddede Bu Makale

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Amaç & Hipotez:In this paper we prove two fixed point theorems in compact cone metricspaces over normal cones.
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Temel Bulgular & Veri:The first theorem generalizes Edelstein theorem [8] and is different from the generalization obtained in [11].
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Sonuç & Katkı:Moreover, different versions of the two theorems are proved in TVS-cone metric spacesby making use of the nonlinear scalarization function used very recentlyby Wei-Shih Du in [A note on cone metric fixed point theory and itsequivalence, Nonlinear Analysis,72(5),2259-2261 (2010).] to prove theequivalence of the Banach contraction principle in cone metric spacesand usual metric spaces.
🔬Tür:Araştırma Makalesi
📍Kapsam:2010 Verileri
⚙️Değişkenler:Alan Parametreleri

Abstract

In this paper we prove two fixed point theorems in compact cone metricspaces over normal cones. The first theorem generalizes Edelstein theorem [8] and is different from the generalization obtained in [11]. Thesecond theorem generalizes the main result in [10] and the first theorem.However, the two theorems fail in different categories. Moreover, different versions of the two theorems are proved in TVS-cone metric spacesby making use of the nonlinear scalarization function used very recentlyby Wei-Shih Du in [A note on cone metric fixed point theory and itsequivalence, Nonlinear Analysis,72(5),2259-2261 (2010).] to prove theequivalence of the Banach contraction principle in cone metric spacesand usual metric spaces.

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Bu Makaleye Atıf Yap

ABDELJAWAD, T. (2022). Edelstein-type fixed point theorems in compact TVS-cone metric spaces. Hacettepe Journal of Mathematics and Statistics, Cilt: 43 - Sayı: 4, 561–569. https://ajindex.com/articles/530385

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Kaynakça (17)

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