• 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.

• Nonlinear Functional Analysis and Applications
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• v.26 no.5
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• pp.1059-1075
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• 2021

In this paper, we unify and enrich the well-known classical metrical coincidence theorems on a complete metric space due to Machuca, Goebel and Jungck. We further extend our newly proved results on a subspace Y of metric space X, wherein X need not be complete. Finally, we slightly modify the existing results involving (E.A)-property and (CLR_g)-property and apply these results to deduce our coincidence and common fixed point theorems.

• Korean Journal of Mathematics
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• v.31 no.4
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• pp.391-403
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• 2023

In this work, we establish common fixed point results by utilizing a variant of F-contraction in the framework of C^*-algebra valued metric spaces. We utilize E.A. and C.L.R. property possessed by the mappings to prove common fixed point results in the same metric settings. To validate the applicability of these common fixed point results, we provide illustrative examples too.

• East Asian mathematical journal
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• v.24 no.2
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• pp.169-176
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• 2008

The aim of this paper is to prove a common fixed point theorem in normed linear spaces for noncompatible, discontinuous mappings without assuming completeness of the space. We also give an application of our theorem to best approximation theory.

• East Asian mathematical journal
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• v.25 no.2
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• pp.179-196
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• 2009

Let E be a uniformly convex Banach space and K a nonempty closed convex subset which is also a nonexpansive retract of E. For i = 1, 2, 3, let $T_i:K{\rightarrow}E$ be an asymptotically nonexpansive mappings with sequence ${\{k_n^{(i)}\}\subset[1,{\infty})$ such that $\sum_{n-1}^{\infty}(k_n^{(i)}-1)$ < ${\infty},\;k_{n}^{(i)}{\rightarrow}1$, as $n{\rightarrow}\infty$ and F(T)=$\bigcap_{i=3}^3F(T_i){\neq}{\phi}$ (the set of all common xed points of $T_i$, i = 1, 2, 3). Let {$a_n$},{$b_n$} and {$c_n$} are three real sequences in [0, 1] such that $\in{\leq}\;a_n,\;b_n,\;c_n\;{\leq}\;1-\in$ for $n{\in}N$ and some ${\in}{\geq}0$. Starting with arbitrary $x_1{\in}K$, define sequence {$x_n$} by setting {$$x_{n+1}=P((1-a_n)x_n+a_nT_1(PT_1)^{n-1}y_n)$$ $$y_n=P((1-b_n)x_n+a_nT_2(PT_2)^{n-1}z_n)$$ $$z_n=P((1-c_n)x_n+c_nT_3(PT_3)^{n-1}x_n)$$. Assume that one of the following conditions holds: (1) E satises the Opial property, (2) E has Frechet dierentiable norm, (3) $E^*$ has Kedec -Klee property, where $E^*$ is dual of E. Then sequence {$x_n$} converges weakly to some p${\in}$F(T).

• Honam Mathematical Journal
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• v.36 no.1
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• pp.157-165
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• 2014

In this paper, we obtain some common fixed point theorems of single and multivalued maps under hybrid contractive conditions satisfying weakly commuting in IFMS. Our results extend previous ones in IFMS.

• Journal of applied mathematics & informatics
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• v.24 no.1_2
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• pp.437-448
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• 2007

Suppose K is a nonempty closed convex nonexpansive retract of a real uniformly convex Banach space E with P as a nonexpansive retraction. Let $T_1,\;T_2\;and\;T_3\;:\;K{\rightarrow}E$ be nonexpansive mappings with nonempty common fixed points set. Let $\{\alpha_n\},\;\{\beta_n\},\;\{\gamma_n\},\;\{\alpha'_n\},\;\{\beta'_n\},\;\{\gamma'_n\},\;\{\alpha'_n\},\;\{\beta'_n\}\;and\;\{\gamma'_n\}$ be real sequences in [0, 1] such that ${\alpha}_n+{\beta}_n+{\gamma}_n={\alpha}'_n+{\beta'_n+\gamma}'_n={\alpha}'_n+{\beta}'_n+{\gamma}'_n=1$, starting from arbitrary $x_1{\in}K$, define the sequence $\{x_n\}$ by $$\{zn=P({\alpha}'_nT_1x_n+{\beta}'_nx_n+{\gamma}'_nw_n)\;yn=P({\alpha}'_nT_2z_n+{\beta}'_nx_n+{\gamma}'_nv_n)\;x_{n+1}=P({\alpha}_nT_3y_n+{\beta}_nx_n+{\gamma}_nu_n)$$ with the restrictions $\sum^\infty_{n=1}{\gamma}_n<\infty,\;\sum^\infty_{n=1}{\gamma}'_n<\infty,\; \sum^\infty_{n=1}{\gamma}'_n<\infty$. (i) If the dual $E^*$ of E has the Kadec-Klee property, then weak convergence of a $\{x_n\}$ to some $x^*{\in}F(T_1){\cap}{F}(T_2){\cap}(T_3)$ is proved; (ii) If $T_1,\;T_2\;and\;T_3$ satisfy condition(A'), then strong convergence of $\{x_n\}$ to some $x^*{\in}F(T_1){\cap}{F}(T_2){\cap}(T_3)$ is obtained.

• East Asian mathematical journal
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• v.28 no.5
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• pp.543-552
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• 2012

The aim of this paper is to prove a common fixed point theorem in normed linear spaces for discontinuous, occasionally weakly biased mappings without assuming completeness of the space. We give an example to illustrare our theorem. We also give an application of our theorem to best approximation theory. Our theorem improve the results of Gregus [9], Jungck [12], Pathak, Cho and Kang [22], Sharma and Deshpande [26]-[28].

• Proceedings of the IEEK Conference
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• 2004.08c
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• pp.499-502
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• 2004

A two-stage Class E power amplifier operated at 2.44GHz is designed in 0.25-$\mu$m CMOS process for Class-l Bluetooth application. The power amplifier employs c1ass-E topology to exploit its soft-switching property for high efficiency. A preamplifter with common-mode configuration is used to drive the output-stage of Class-E type. The amplifier delivers 20-dBm output power with 70$\%$ PAE (power -added-efficiency) at 2-V supply voltage.

• Proceedings of the Korean Society for Agricultural Machinery Conference
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• 2017.04a
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• pp.110-110
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• 2017

Biological systems offer unique principles for the design and fabrication of engineering platforms (i.e., popularly known as "Biomimetics") for various applications in many fields. For example, the lotus leaves exhibit unique surfaces consisting of evenly distributed micro and nanostructures. These unique surfaces of lotus leaves have the ability of superhydrophobic property to avoid getting wet by the surrounding water (i.e., Lotus effect). Inspired by the surface topographies of lotus leaves, the artificial superhydrophobic surfaces were developed using various micro- and nanoengineering. Here, we propose new platforms that can control hydrophilic and hydrophobic property of surfaces by mimicking micro- and nanosurfaces of various natural leaves such as common camellia, hosta plantaginea, and lotus. Using capillary force lithography technology and polymers in combination with biomimetic design principle, the unique micro- and nanostructures mimicking natural surfaces of common camellia, hosta plantaginea, and lotus were designed and fabricated. We also demonstrated that the replicated polymeric surfaces had different hydrophilic and hydrophobic properties according to the mimicking the natural leaf surfaces, which could be used as a simple, but powerful methodology for design and fabrication of controlled hydrophilic and hydrophobic platforms for various applications in the field of agriculture and biological engineering.