Cone metric spaces and fixed point theorems in diametrically contractive mappings

Türkoğlu, Duran; Abuloha, Muhib

doi:10.1007/s10114-010-8019-5

Cited by 76 publications

(48 citation statements)

References 5 publications

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“…Ada banyak sifat topologi, salah satunya adalah aksioma keterhitungan pertama. Turkoglu & Abuloha pada [7] telah membuktikan bahwa setiap ruang metrik kerucut adalah ruang hitung pertama. Menggunakan hasil pada [2] Badrulfalah, Khafsah J, dan Iin Irianingsih pada [1] telah melakukan penelitian permulaan tentang aksioma keterhitungan pertama pada topologi hasil kali dua ruang metrik kerucut.…”

Section: Pendahuluanunclassified

Sub Ruang Tutup Topologi Hasil Kali Ruang Metrik Kerucut

Badrulfalah¹

2018

EKSAKTA

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Sebuah sifat topologi selain dapat dimiliki oleh suatu ruang topologi juga dapat dimiliki oleh subruang dari ruang topologi tersebut. Pada makalah ini akan dibahas tentang aksioma keterhitungan pertama pada topologi hasil kali ruang metrik kerucut, khususnya pada subruang tutup. Pembahasan dilakukan dengan menunjukkan bahwa setiap elemen dari setiap subruang tutup dari topologi hasil kali dua ruang metrik kerucut memiliki basis lokal terhitung. Hasilnya adalah setiap subruang tutup dari topologi hasil kali ruang metrik kerucut juga memenuhi aksioma keterhitungan pertama. Dengan kata lain keterhitungan pertama bersifat hereditas lemah.

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Section: Pendahuluanunclassified

Sub Ruang Tutup Topologi Hasil Kali Ruang Metrik Kerucut

Badrulfalah¹

2018

EKSAKTA

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“…[19] Every cone metric space (X, d) is a topological space. For c 0, c ∈ E, x ∈ X, let B(x, c) = {y ∈ X : d(y, x) c} and β = {B(x, c) : x ∈ X, c 0}.…”

Section: Definition 22mentioning

confidence: 99%

“…[19] Let (X, d) be a cone metric space, and T : (X, d) → (X, d) be any map. Then, T is continuous if and only if T is sequentially continuous.…”

Section: Definition 22mentioning

confidence: 99%

“…Then, several authors have studied fixed point problems in cone metric spaces. For some of the work on cone metric spaces, one may refer to [1,5,7,8,19]. Bhaskar and Lakshmikantham [4] introduced the notion of a coupled fixed point of a mapping F from X × X into X. Lakshmikantham andĆirić [11] introduced the concept of coupled coincidence points and proved coupled coincidence and coupled common fixed point results for mappings F from X × X into X and g from X into X satisfying nonlinear contraction in ordered metric space.…”

Section: Introductionmentioning

confidence: 99%

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Coupled coincidence point theorems for mappings without mixed monotone property under c-distance in cone metric spaces

Batra¹,

Vashistha²,

Kumar³

2014

J. Nonlinear Sci. Appl.

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Fixed point theory in the field of partially ordered metric spaces has been an area of attraction since the appearance of Ran and Reurings theorem and Nieto and Rodríguez-López theorem. One of the most significant hypotheses of these theorems was the mixed monotone property which has been avoided and replaced by the notion of invariant set in recent years and many statements have been proved using the concept of invariant set. In this paper we show that the invariant condition guides us to prove many similar results to which we were exposed to using the mixed monotone property. We present some examples in support of applicability of our results.

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“…After that series of articles about cone metric spaces started to appear. Some of those articles dealt with the extension of certain fixed point theorems to cone metric spaces see, e.g., 2-5 , and some other with the structure of the spaces themselves see, e.g., 3,6 . Very recently, some authors have used regular cones to extend some fixed point theorems.…”

Section: Introductionmentioning

confidence: 99%

Quasicone Metric Spaces and Generalizations of Caristi Kirk's Theorem

Abdeljawad¹,

Karapınar²

2009

Fixed Point Theory Appl

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Cone-valued lower semicontinuous maps are used to generalize Cristi-Kirik's fixed point theorem to Cone metric spaces. The cone under consideration is assumed to be strongly minihedral and normal. First we prove such a type of fixed point theorem in compact cone metric spaces and then generalize to complete cone metric spaces. Some more general results are also obtained in quasicone metric spaces.

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Cone metric spaces and fixed point theorems in diametrically contractive mappings

Cited by 76 publications

References 5 publications

Sub Ruang Tutup Topologi Hasil Kali Ruang Metrik Kerucut

Sub Ruang Tutup Topologi Hasil Kali Ruang Metrik Kerucut

Coupled coincidence point theorems for mappings without mixed monotone property under c-distance in cone metric spaces

Quasicone Metric Spaces and Generalizations of Caristi Kirk's Theorem

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