• East Asian mathematical journal
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• v.27 no.5
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• pp.557-564
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• 2011

In 2007, Huang and Zhang [1] introduced a cone metric space with a cone metric generalizing the usual metric space by replacing the real numbers with Banach space ordered by the cone. They considered some fixed point theorems for contractive mappings in cone metric spaces. Since then, the fixed point theory for mappings in cone metric spaces has become a subject of interest in [1-6] and references therein. In this paper, we consider some fixed point theorems for generalized nonexpansive setvalued mappings under suitable conditions in sequentially compact cone metric spaces and complete cone metric spaces.

• The Pure and Applied Mathematics
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• v.30 no.1
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• pp.1-13
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• 2023

In this paper, we introduce double controlled cone metric spaces via two control functions. An example of a double controlled cone metric space by two incomparable functions, which is not a controlled metric space, is given. We also provide some fixed point results involving Banach type and Kannan type contractions in the setting of double controlled cone metric spaces.

• Journal of the Korean Mathematical Society
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• v.50 no.1
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• pp.95-109
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• 2013

The aim of this paper is to establish variational principle on cone metric spaces and to give some existence theorems of solutions for equilibrium problems on cone metric spaces. We give some equivalences of an existence theorem of solutions for equilibrium problems on cone metric spaces.

• Honam Mathematical Journal
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• v.43 no.2
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• pp.305-323
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• 2021

In the present paper, utilizing (𝜙, 𝜓)-weak contractive conditions, unique fixed point and some coincidence point results have been studied in the context of cone 2- metric spaces. Also, our obtained results generalize some results from cone metric space to cone 2-metric space. For the authenticity of the presented work, a non trivial example is also provided.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.39-46
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• 2017

In this paper, we propose a new multistep iteration for a finite family of asymptotically quasi-nonexpansive mappings in convex cone metric spaces. Then we show that our iteration converges to a common fixed point of this class of mappings under suitable conditions. Our result generalizes the corresponding result of Lee [5] from the closed convex subset of a convex cone metric space to whole space.

• Korean Journal of Mathematics
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• v.20 no.3
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• pp.353-360
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• 2012

In this paper we introduce the property (C), which is a cone metric extension of the usual metric property (E,A) and consider fixed point theorems for generalized contractive mappings under suitable conditions in cone metric spaces without normal cones.

• Journal of the Korean Mathematical Society
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• v.55 no.6
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• pp.1513-1528
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• 2018

The aim of this paper is to introduce the concept of generalized cone metric spaces over Banach algebras as a generalization of generalized metric spaces and present several fixed point results of a class of contractive mappings in generalized cone metric spaces over Banach algebras. Moreover, in order to support our main results, one example is given at the end of this paper.

• Communications of the Korean Mathematical Society
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• v.32 no.1
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• pp.65-74
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• 2017

In this paper, we establish a unique common fixed point theorem for T-contraction of two self maps on generalized cone b-metric spaces with solid cone. The result of this paper improves and generalizes several well-known results in the literature. Two examples are also given to support the result.

• East Asian mathematical journal
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• v.37 no.1
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• pp.123-130
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• 2021

In this paper, we introduce the new concept of a cone metric-like space and consider some fixed point theorems for generalized contractive mappings under suitable conditions in cone metric-like spaces. Our results generalize and unify the several main results of [1, 2, 9].

• Journal of the Chungcheong Mathematical Society
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• v.35 no.1
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• pp.91-101
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• 2022

We study some properties of nonwandering set Ω(𝜙) and chain recurrent set CR(𝜙) for an expansive flow which has the POTP on a compact TVS-cone metric spaces. Moreover we shall prove a spectral decomposition theorem for an expansive flow which has the POTP on TVS-cone metric spaces.