• 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.

• 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.

• East Asian mathematical journal
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• v.32 no.5
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• pp.677-684
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• 2016

In this paper, the notion of S-metric spaces will be introduced. We present some fixed point theorems for two maps on complete S-metric spaces and an illustrative example is given for the single-valued case. By using the similar method as in [4], a common fixed point theorem for two single-valued mappings is obtained in S-metric spaces.

• Korean Journal of Mathematics
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• v.32 no.1
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• pp.109-120
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• 2024

The aim of this research is to describe lacunary ∆^m-statistically convergent sequences with respect to metrics on generalised metric spaces (g-metric spaces) and to look into the fundamental characteristics of this statistical form of convergence. Also, the relationship between strong summability and lacunary ∆^m-statistical convergence in g-metric space is established at the end.

• Journal of the Korean Mathematical Society
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• v.51 no.6
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• pp.1189-1207
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• 2014

A partial metric, also called a nonzero self-distance, is motivated by experience from computer science. Besides a lot of properties of partial metric analogous to those of metric, fixed point theorems in partial metric spaces have been studied recently. We establish several kinds of extended fixed point theorems in ordered partial metric spaces with higher dimension under generalized notions of mixed monotone mappings.

• 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.

• East Asian mathematical journal
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• v.17 no.2
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• pp.191-195
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• 2001

The purpose of this note is to introduce various metrics and to prove the properties of given metric spaces.

• Nonlinear Functional Analysis and Applications
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• v.26 no.1
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• pp.165-175
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• 2021

In this article we derive some best approximation theorems for multimaps in abstract convex metric spaces. We are based on generalized KKM maps due to Kassay-Kolumbán, Chang-Zhang, and studied by Park, Kim-Park, Park-Lee, and Lee. Our main results are extensions of a recent work of Mitrović-Hussain-Sen-Radenović on G-convex metric spaces to partial KKM metric spaces. We also recall known works related to single-valued maps, and introduce new partial KKM metric spaces which can be applied our new results.

• Korean Journal of Mathematics
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• v.30 no.4
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• pp.603-614
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• 2022

The main intent of this paper is to prove an existence and uniqueness fixed point result under Geraghty contractions in b-metric-like spaces, which remains an extended version of corresponding results in b-metric spaces and metriclike spaces. Using two types of Geraghty contractions, an approach is adopted to verify some fixed point results in b-metric-like spaces. Our main result is an extension of an earlier result given by Geraghty in b-metric-like-space. An example is also provided to demonstrate the validity of our main result. Moreover, as an application of our main result, the existence of solution of a Fredholm integral equation is established which may further be utilized to study the seismic response of dams during earthquakes.

• Journal of applied mathematics & informatics
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• v.41 no.1
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• pp.205-214
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• 2023

A multi-dimensional metric, called a g-metric, as a generalization of the G-metric was introduced. We establish some well-known fixed point theorems in the frame work of g-metric spaces.