• Bulletin of the Korean Mathematical Society
• /
• v.48 no.3
• /
• pp.575-584
• /
• 2011

In Shahzad and Zegeye [Nonlinear Anal. 71 (2009), no. 3-4, 838-844], the authors introduced several Ishikawa iterative schemes for xed points of multi-valued mappings in Banach spaces, and proved some strong convergence theorems by using their iterations. In their proofs of the main results, it seems reasonable and simpler to prove for the iteration {$x_n$} to be a Cauchy sequence. In this paper, we modify and improve the proofs of the main results given by Shahzad and Zegeye. Two concrete examples also are given.

• Bulletin of the Korean Mathematical Society
• /
• v.39 no.1
• /
• pp.43-51
• /
• 2002

The aim of this paper is to prove a convergence theorem of a generalized Ishikawa iteration sequence for two multi-valued strongly pseudo-contractive mappings by using an approximation method in real uniformly smooth Banach spaces. We generalize and extend the results of Chang and Chang, Cho, Lee, Jung, and Kang.

• International Journal of Fuzzy Logic and Intelligent Systems
• /
• v.11 no.2
• /
• pp.108-112
• /
• 2011

Kaneko et a1.[4] etc many authors extended with multi-valued maps for the notion of compatible maps in complete metric space. Recently, O'Regan et a1.[5] presented fixed point and homotopy results for compatible single-valued maps on complete metric spaces. In this paper, we will establish some common fixed point theorems using compatible maps in intuitionistic fuzzy metric space.

• Korean Journal of Mathematics
• /
• v.32 no.3
• /
• pp.507-520
• /
• 2024

In this manuscript, a new multi-valued contraction is defined from a combination of Jaggi-type hybrid contraction and Suzuku-type hybrid contraction. Conditions for the existence of fixed points for such contractions in metric space are investigated. Moreover, some consequences are highlighted and discussed to indicate the significance of our proposed ideas. An example is given to support the assumptions of our theorems.

• Journal of the Institute of Electronics Engineers of Korea TC
• /
• v.37 no.1
• /
• pp.1-11
• /
• 2000

We propose a predistorter to compensate for nolinear distortion induced by a high power amplifier employed in multi carrier-code division multiple access (MC-CDMA) systems. The proposed scheme rests upon the fixed point iteration (FPI) associated with the contraction mapping theorem. Unlike the predistorter based on the FPI already presented by the authors in other literatures which operates on complex-valued modulation signals, the proposed predistorter in this paper deals with real-valued FPI on modulation signal amplitudes, resulting in less complexity. Simulation results on a BPSK-modulated, 64-subcarrier synchronous MC-CDMA baseband system with a traveling wave tube amplifier in the transmitter, indicate that the proposed predistorter achieves significant improvement in terms of bit error rate and total degradation over those without the predistorter. Moreover, the proposed predistorter outperforms the complex-valued counterpart, in particular, for small output back-off levels.

• Communications of the Korean Mathematical Society
• /
• v.25 no.3
• /
• pp.427-441
• /
• 2010

In this paper, we study the behavior and sensitivity analysis of the solution set for a new system of generalized parametric multi-valued variational inclusions with (A, $\eta$)-accretive mappings in q-uniformly smooth Banach spaces. The present results improve and extend many known results in the literature.

• Bulletin of the Korean Mathematical Society
• /
• v.29 no.1
• /
• pp.81-87
• /
• 1992

Wellknown invariance of domain theorems are Brower's invariance of domain theorem for continuous mappings defined on a finite dimensional space and Schauder-Leray's invariance of domain theorem for the class of mappings I+C defined on a infinite dimensional Banach space with I the identity and C compact. The two classical invariance of domain theorems were proved by applying the homotopy invariance of Brower's degree and Leray-Schauder's degree respectively. Degree theory for some class of mappings is a useful tool for mapping theorems. And mapping theorems (or surjectivity theorems of mappings) are closely related with invariance of domain theorems for mappings. In[4, 5], Browder and Petryshyn constructed a multi-valued degree theory for A-proper mappings. From this degree Petryshyn [9] obtained some invariance of domain theorems for locally A-proper mappings. Recently Browder [6] has developed a degree theory for demicontinuous mapings of type ( $S_{+}$) from a reflexive Banach space X to its dual $X^{*}$. By applying this degree we obtain some invariance of domain theorems for demicontinuous mappings of type ( $S_{+}$). ( $S_{+}$).

• Proceedings of the Korean Institute of Intelligent Systems Conference
• /
• 1996.10a
• /
• pp.253-256
• /
• 1996

Rainfall is one of the major and complicated elements of hydrologic system. Accurate prediction of rainfall is very important to mitigate storm damage. The neural network is a good model to be applied for the classification problem, large combinatorial optimization and nonlinear mapping. In this dissertation, rainfall predictions by the neural network theory were presented. A multi-layer neural network was constructed. The network learned continuous-valued input and output data. The network was used to predict rainfall. The online, multivariate, short term rainfall prediction is possible by means of the developed model. A multidimensional rainfall generation model is applied to Seoul metropolitan area in order to generate the 10-minute rainfall. Application of neural network to the generated rainfall shows good prediction. Also application of neural network to 1-hour real data in Seoul metropolitan area shows slightly good predictions.

• Nonlinear Functional Analysis and Applications
• /
• v.29 no.2
• /
• pp.477-485
• /
• 2024

In this work, we will generalize the notion of multivalued (ν, 𝒞)-contraction mapping in 𝑏-Menger spaces and we shall give a new fixed point result of this type of mappings. As a consequence of our main result, we obtained the corresponding fixed point theorem in fuzzy 𝑏-metric spaces. Also, an example will be given to illustrate the main theorem in ordinary 𝑏-metric spaces.

• Nonlinear Functional Analysis and Applications
• /
• v.28 no.2
• /
• pp.497-520
• /
• 2023

Numerous problems in science and engineering defined by nonlinear functional equations can be solved by reducing them to an equivalent fixed point problem. Fixed point theory provides essential tools for solving problems arising in various branches of mathematical analysis, such as split feasibility problems, variational inequality problems, nonlinear optimization problems, equilibrium problems, complementarity problems, selection and matching problems, and problems of proving the existence of solution of integral and differential equations.The theory of fixed is known to find its applications in many fields of science and technology. For instance, the whole world has been profoundly impacted by the novel Coronavirus since 2019 and it is imperative to depict the spread of the coronavirus. Panda et al. [24] applied fractional derivatives to improve the 2019-nCoV/SARS-CoV-2 models, and by means of fixed point theory, existence and uniqueness of solutions of the models were proved. For more information on applications of fixed point theory to real life problems, authors should (see [6, 13, 24] and the references contained in).