• 대한수학회지
• /
• 제41권4호
• /
• pp.667-680
• /
• 2004

We generalize a theorem of W. Benz by proving the following result: Let $H_{\theta}$ be a half space of a real Hilbert space with dimension $\geq$ 3 and let Y be a real normed space which is strictly convex. If a distance $\rho$ > 0 is contractive and another distance N$\rho$ (N $\geq$ 2) is extensive by a mapping f : $H_{\theta}$ \longrightarrow Y, then the restriction f│$_{\theta}$ $H_{+}$$\rho$/2// is an isometry, where $H_{\theta}$＋$\rho$/2/ is also a half space which is a proper subset of $H_{\theta}$. Applying the above result, we also generalize a classical theorem of Beckman and Quarles.

• Nonlinear Functional Analysis and Applications
• /
• 제26권5호
• /
• pp.917-933
• /
• 2021

In this paper, we investigate the behavior and sensitivity analysis of a solution set for a parametric generalized multi-valued nonlinear quasi-variational inclusion problem in a real Hilbert space. For this study, we utilize the technique of resolvent operator and the property of a fixed-point set of a multi-valued contractive mapping. We also examine Lipschitz continuity of the solution set with respect to the parameter under some appropriate conditions.

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

• 한국방송∙미디어공학회:학술대회논문집
• /
• 한국방송공학회 1996년도 Proceedings International Workshop on New Video Media Technology
• /
• pp.72-76
• /
• 1996

We propose a novel algorithm for fractal video sequence coding, based on the circular prediction mapping (CPM), in which each range block is approximated by a domain block in the circularly previous frame. In our approach, the size of the domain block is set to be same as that of the range block for exploiting the high temporal correlation between the adjacent frames, while most other fractal coders use the domain block larger than the range block. Therefore the domain-range mapping in the CPM is similar to the block matching algorithm in the motion compensation techniques, and the advantages of this similarity are discussed. Also we show that the CPM can be combined with non-contractive inter-frame mapping (NCIM), improving the performance of the fractal sequence coder further. The computer simulation results on real image sequences demonstrate that the proposed algorithm provides very promising performance at low bit-rate, ranging from 40 Kbps to 250 Kbps.

• 한국수학교육학회지시리즈B:순수및응용수학
• /
• 제18권3호
• /
• pp.201-217
• /
• 2011

The aim of this paper is to define a new commutativity condition for a pair of self mappings i.e., (DS)-weak commutativity condition, which is weaker that compatibility of mappings in the settings of intuitionistic Menger spaces. We show that a common fixed point theorem can be proved for nonlinear contractive condition in intuitionistic Menger spaces without assuming continuity of any mapping. To prove the result we use (DS)-weak commutativity condition for mappings. We also give examples to validate our results.

• 산업기술연구
• /
• 제15권
• /
• pp.93-101
• /
• 1995

Fractal coding is a promising method for image compression, but it has not lived up to its promise as low bit-rate image compression scheme. The existing algorithms for finding self-mapping contractive transforms are computationally expensive and offer a poor rate-quality tradeoff. In this paper, we propose a segment based fractal coding. We classify the range blocks into shade, midrange or edge blocks, and segment edge block along the edge. And we apply midrange coding scheme for each segment. Our experiments show that our method gives better rate-qualty trade of than current fractal block coding methods.

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

• East Asian mathematical journal
• /
• 제27권5호
• /
• pp.557-564
• /
• 2011

In 2007, Huang and Zhang [1] introduced a cone metric space with a cone metric generalizing the usual metric space by replacing the real numbers with Banach space ordered by the cone. They considered some fixed point theorems for contractive mappings in cone metric spaces. Since then, the fixed point theory for mappings in cone metric spaces has become a subject of interest in [1-6] and references therein. In this paper, we consider some fixed point theorems for generalized nonexpansive setvalued mappings under suitable conditions in sequentially compact cone metric spaces and complete cone metric spaces.

• 한국지능시스템학회논문지
• /
• 제18권4호
• /
• pp.524-529
• /
• 2008

Park et.al.[10] defined the intuitionistic fuzzy metric space in which it is a little revised in Park[4], and Park et.a1.[7] proved a fixed point theorem of Banach for the contractive mapping of a complete intuitionistic fuzzy metric space. In this paper, we will establish common fixed point theorem for four self maps in intuitionistic fuzzy metric space. These results have been used to obtain translation and generalization of Grabiec's contraction principle.

• 대한수학회논문집
• /
• 제34권4호
• /
• pp.1201-1222
• /
• 2019

In this paper, we introduce the notion of modified TAC-Suzuki-Berinde type F-contraction and modified TAC-(${\psi}$, ${\phi}$)-Suzuki type rational mappings in the frame work of complete metric spaces, we also establish some fixed point results regarding this class of mappings and we present some examples to support our main results. The results obtained in this work extend and generalize the results of Dutta et al. [9], Rhoades [18], Doric, [8], Khan et al. [13], Wardowski [25], Piri et al. [17], Sing et al. [23] and many more results in this direction.