• 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.

• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.289-308
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• 2022

In this paper, we introduce the concept of M^*-metric spaces and how much the M^*-metric and the b-metric spaces are related. Moreover, we introduce some ways of generating M^*-metric spaces. Also, we investigate some types of convergence associated with M^*-metric spaces. Some common fixed point for contraction and generalized contraction mappings in M^*-metric spaces. Our work has been supported by many examples and an application.

• Journal of applied mathematics & informatics
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• v.27 no.1_2
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• pp.351-363
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• 2009

In this paper, we give some new definitions of $D^*$-metric spaces and we prove a common fixed point theorem for six mappings under the condition of weakly compatible mappings in complete $D^*$-metric spaces. We get some improved versions of several fixed point theorems in complete $D^*$-metric spaces.

• Journal of the Chungcheong Mathematical Society
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• v.33 no.4
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• pp.387-394
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• 2020

Matthews introduced the concepts of partial metric spaces and proved the Banach fixed point theorem in complete partial metric spaces. Dukic, Kadelburg, and Radenovic proved fixed point theorems for Geraghty-type mappings in complete partial metric spaces. In this paper, we prove the fixed point theorem for some contractive mapping in a complete partial metric space.

• East Asian mathematical journal
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• v.25 no.1
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• pp.107-117
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• 2009

In this paper, we give some new definitions of D-metric spaces and we prove a common fixed point theorem for a class of mappings under the condition of weakly compatible mappings in complete D-metric spaces. We get some improved versions of several fixed point theorems in complete D-metric spaces.

• The Pure and Applied Mathematics
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• v.30 no.2
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• pp.169-190
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• 2023

In this paper, we introduce an extension of rectangular metric spaces called controlled rectangular metric spaces, by changing the rectangular inequality in the definition of a metric space. We also establish some fixed point theorems for self-mappings defined on such spaces. Our main results extends and improves many results existing in the literature. Moreover, an illustrative example is presented to support the obtained results.

• Journal of the Chungcheong Mathematical Society
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• v.23 no.4
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• pp.645-656
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• 2010

In this paper, we prove a common fixed point theorem for four mappings on fuzzy 2-metric spaces. Our result is an extension of results of S. H. Cho [2] to fuzzy 2-metric spaces. Also, it is a generalization of a result of S. Sharma [11].

• Nonlinear Functional Analysis and Applications
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• v.27 no.2
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• pp.233-247
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• 2022

In the present manuscript, we employ the concepts of Θ-map and Φ-map to define a strong (𝜃, 𝜙)s-contraction of a map f in a b-metric space (M, d_b). Then we prove and derive many fixed point theorems as well as we provide an example to support our main result. Moreover, we utilize our results to obtain many results in the settings of metric and G-metric spaces. Our results improve and modify many results in the literature.

• Nonlinear Functional Analysis and Applications
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• v.28 no.3
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• pp.753-774
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• 2023

The fundamental aim of the proposed work is to introduce the concept of soft rectangular b-metric spaces, which involves generalizing the notions of rectangular metric spaces and b-metric spaces. Furthermore, an investigation into specific characteristics and topological aspects of the underlying generalization of metric spaces is conducted. Moreover, the research establishes fixed point theorems for mappings that satisfy essential criteria within soft rectangular b-metric spaces. These theorems offer a broader perspective on established results in fixed point theory. Additionally, several congruous examples are presented to enhance the understanding of the introduced spatial framework.

• The Pure and Applied Mathematics
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• v.26 no.4
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• pp.215-231
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• 2019

In this paper, we establish some ĆIRIC type fixed point theorems in α-complete and orbitally T-complete non-Archimedean modular metric spaces. Meanwhile, we present an illustrative example to emphasis the realized improvements. These obtained results extend and improve certain well known results in the literature.