• East Asian mathematical journal
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• 제31권1호
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• pp.65-75
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• 2015

In modern times, coupled fixed point theorems have been rigorously studied by many researchers in the milieu of partially ordered G-metric spaces using different contractive conditions. In this note, some coupled fixed point theorems using mixed monotone property in partially ordered G-metric spaces are obtained. Furthermore some theorems by omitting the completeness on the space and continuity conditions on function, are obtained. Our results partially generalize some existing results in the present literature. To exemplify our results and to distinguish them from the existing ones, we equip the article with suitable examples.

• Kyungpook Mathematical Journal
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• 제45권3호
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• pp.433-443
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• 2005

In 1994, Lim-Xu asked whether the Maluta's constant D(X) < 1 implies the fixed point property for asymptotically nonexpansive mappings and gave a partial solution for this question under an additional assumption for T, i.e., weakly asymptotic regularity of T. In this paper, we shall prove that the result due to Lim-Xu is also satisfied for more general non-Lipschitzian mappings in reflexive Banach spaces with weak uniform normal structure. Some applications of this result are also added.

• Nonlinear Functional Analysis and Applications
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• 제27권3호
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• pp.569-585
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• 2022

A brief comparative survey of some generalizations of a metric space with three dimensional metric structures and different forms of the triangle inequality is done along with their topological properties. Then a common fixed point is obtained for reciprocally continuous and compatible self-maps in a G-metric space. Further, a common fixed point theorem is proved for a pair of weakly compatible self-maps on a G-metric space with the common limit range property.

• East Asian mathematical journal
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• 제24권1호
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• pp.81-95
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• 2008

Let E be a uniformly convex Banach space with a uniformly $G{\hat{a}}teaux$ differentiable norm, C a nonempty closed convex subset of E, and $T\;:\;C\;{\rightarrow}\;E$ a nonexpansive mapping satisfying the weak inwardness condition. Assume that every weakly compact convex subset of E has the fixed point property. For $f\;:\;C\;{\rightarrow}\;C$ a contraction and $t\;{\in}\;(0,\;1)$, let $x_t$ be a unique fixed point of a contraction $T_t\;:\;C\;{\rightarrow}\;E$, defined by $T_tx\;=\;tf(x)\;+\;(1\;-\;t)Tx$, $x\;{\in}\;C$. It is proved that if {$x_t$} is bounded, then $x_t$ converges to a fixed point of T, which is the unique solution of certain variational inequality. Moreover, the strong convergence of other implicit and explicit iterative schemes involving the sunny nonexpansive retraction is also given in a reflexive and strictly convex Banach space with a uniformly $G{\hat{a}}teaux$ differentiable norm.

• 한국수학교육학회지시리즈A:수학교육
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• 제24권1호
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• pp.1-3
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• 1985

• Nonlinear Functional Analysis and Applications
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• 제27권4호
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• pp.709-730
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• 2022

We consider the nonlinear matrix equation (NMEs) of the form 𝓤 = 𝓠 + Σ^k_i=1 𝓐^*_iℏ(𝓤)𝓐_i, where 𝓠 is n × n Hermitian positive definite matrices (HPDS), 𝓐₁, 𝓐₂, . . . , 𝓐_m are n × n matrices, and ~ is a nonlinear self-mappings of the set of all Hermitian matrices which are continuous in the trace norm. We discuss a sufficient condition ensuring the existence of a unique positive definite solution of a given NME and demonstrate this sufficient condition for a NME 𝓤 = 𝓠 + 𝓐^*₁(𝓤²/900)𝓐₁ + 𝓐^*₂(𝓤²/900)𝓐₂ + 𝓐^*₃(𝓤²/900)𝓐₃. In order to do this, we define 𝓕𝓖_w-contractive conditions and derive fixed points results based on aforesaid contractive condition for a mapping in extended Branciari b-metric distance followed by two suitable examples. In addition, we introduce weak well-posed property, weak limit shadowing property and generalized Ulam-Hyers stability in the underlying space and related results.

• 대한수학회논문집
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• 제11권3호
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• pp.725-742
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• 1996

In this paper we give some sharp expressions of the weakly convergent sequence coefficient WCS(X) of a Banach space X. They are used to prove fixed point theorems for involution mappings T from a weakly compact convex subset C of a Banach space X with WCS(X) > 1 into itself which $T^2$ are both of asymptotically nonexpansive type and weakly asymptotically regular on C. We also show that if X satisfies the semi-Opial property, then every nonexpansive mapping $T : C \to C$ has a fixed point. Further, some questions for asymtotically nonexpansive mappings are raised.

• 대한수학회보
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• 제37권1호
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• pp.21-36
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• 2000

In this article we study the relation between subinvariant submean and normal structure in a locally convex topological vector space. This extends in a natural way a result obtained recently by Lau and Takahashi. Our approach also follows closely theirs.

• 대한수학회지
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• 제54권2호
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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.

• 한국통신학회논문지
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• 제23권9A호
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• pp.2365-2371
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• 1998

이산 여현 변환(Discrete Cosine Transform: DCT)은 음성 및 영상 신호의 압축에 광범위하게 응용되고 있다. 본 논문에서는 $2^{m}$-포인트의 일반적인 경우로 확장이 가능한 새로운 고속 DCT 알고리즘과 구조를 제안한다. 제안한 알고리즘은 커널의 대칭성을 이용하여 N-포인트의 DCT를 N/2-포인트의 DCT로 나누어 처리하며 이를 재귀적으로 적용해 나간다. 제안한 알고리즘은 적은 덧셈 및 곱셈 연산을 통해 변환을 수행하며, 변환을 위해 통과해야 하는 곱셈 연산단의 수가 적고 대부분의 곱셈 연산이 흐름도상의 후반부에서 일괄적으로 수행되므로 고정 소수점 연산시에 발생할 수 있는 오차의 전파를 줄일 수 있다.