• Communications of the Korean Mathematical Society
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• v.34 no.3
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• pp.771-782
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• 2019

We show that mappings preserving unit distance are close to two-isometries. We also prove that a mapping f is a linear isometry up to translation when f is a two-expansive surjective mapping preserving unit distance. Then we apply these results to consider two-isometries between normed spaces, strictly convex normed spaces and unital $C^*$-algebras. Finally, we propose some remarks and problems about generalized two-isometries on Banach spaces.

• The Pure and Applied Mathematics
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• v.22 no.2
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• pp.185-197
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• 2015

The author considers a Noor-type iterative scheme to approximate com- mon fixed points of an infinite family of uniformly quasi-sup(f_n)-Lipschitzian map- pings and an infinite family of g_n-expansive mappings in convex cone metric spaces. His results generalize, improve and unify some corresponding results in convex met- ric spaces [1, 3, 9, 16, 18, 19] and convex cone metric spaces [8].

• Nonlinear Functional Analysis and Applications
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• v.26 no.5
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• pp.949-959
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• 2021

In this paper, some fixed point theorems for new type of (𝜉, 𝛽)-expansive mappings of type (S) and type (T) using control function and 𝛽-admissible function in 𝒢-metric spaces are proved. Further, we prove certain fixed point results by relaxing the continuity condition.

• East Asian mathematical journal
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• v.18 no.1
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• pp.127-136
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• 2002

In this paper we obtain some fixed points theorems of expansive mappings and several necessary and sufficient conditions for the existence of common fixed points of families of self-mappings in metric spaces. Our results generalize and improve the main results of Fisher [1]-[5], Furi-Vignoli [6], $Is\'{e}ki$ [7], Jungck [8], [9], Kashara-Rhoades [10], Liu [13], [14] and Sharma and Strivastava [16].

• Kyungpook Mathematical Journal
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• v.52 no.2
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• pp.155-165
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• 2012

In this paper, we have studied some fixed point theorems on complete G-metric spaces.

• Communications of the Korean Mathematical Society
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• v.25 no.3
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• pp.419-426
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• 2010

In this paper, a three-step iterative method is considered for finding a common element in the set of fixed points of a non-expansive mapping and in the set of solutions of a variational inclusion problem in a real Hilbert space.

• Journal of the Korean Mathematical Society
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• v.54 no.2
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• pp.493-506
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• 2017

In this paper, we define the modulus of n-dimensional U-flatness as the determinant of an $(n+1){\times}(n+1)$ matrix. The properties of the modulus are investigated and the relationships between this modulus and other geometric parameters of Banach spaces are studied. Some results on fixed point theory for non-expansive mappings and normal structure in Banach spaces are obtained.

• Journal of the Korean Mathematical Society
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• v.24 no.1
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• pp.65-71
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• 1987

• Journal of the Chungcheong Mathematical Society
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• v.28 no.3
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• pp.451-463
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• 2015

A continuous and non-decreasing function ${\psi}$ and another continuous function ${\phi}$ with ${\phi}(z)=0{\Leftrightarrow}z=0$ defined on $\mathbb{C}^+=\{x+yi:x,y{\geq}0\}$ are introduced, the ${\psi}-{\phi}$-contractive or expansive type conditions are considered, and the existence theorems of common fixed points for two mappings defined on a complex valued metric space are obtained. Also, Banach contraction principle and a fixed point theorem for a I-expansive type mapping are given on complex valued metric spaces.

• Kyungpook Mathematical Journal
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• v.54 no.1
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• pp.103-111
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• 2014

Let X be a uniformly convex Banach space, and S, T be pair of mean nonexpansive mappings. Some necessary and sufficient conditions are given for Ishikawa iterative sequence converge to common fixed points, and we prove that the sequence of Ishikawa iterations associated with S and T converges to the common fixed point of S and T. This generalizes former results proved by Z. Gu and Y. Li [4].