• East Asian mathematical journal
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• v.31 no.1
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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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• v.45 no.3
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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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• v.27 no.3
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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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• v.24 no.1
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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.

• The Mathematical Education
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• v.24 no.1
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• pp.1-3
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• 1985

• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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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.

• Communications of the Korean Mathematical Society
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• v.11 no.3
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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.

• Bulletin of the Korean Mathematical Society
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• v.37 no.1
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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.

• 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.

• The Journal of Korean Institute of Communications and Information Sciences
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• v.23 no.9A
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• pp.2365-2371
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• 1998

Discrete cosine transform (DCT) has wide applications in speech and image coding. In this paper, we propose a novel fast dCT scheme with the property of reduced multiplication stages and the smaller number of additions and multiplications. This exploits the symmetry property of the DCT kernel to decompose the N-point dCT to N/2 point, and can be generally applied recursively to $2^{m}$-point. The proposed algorithm has a structure that most of multiplications tend to be performed at final stage, and this reduces propagation of truncation error which could occur in the fixed-point computation. Also the minimization of the multiplication stages further decreases the error.