• Communications of the Korean Mathematical Society
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• v.37 no.1
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• pp.259-267
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• 2022

We use L_∞ models to compute the rational homotopy type of the mapping space of the component of the natural inclusion i_n,k : ℂPⁿ ↪ ℂP^n+k between complex projective spaces and show that it has the rational homotopy type of a product of odd dimensional spheres and a complex projective space. We also characterize the mapping aut₁ ℂPⁿ → map(ℂPⁿ, ℂP^n+k; i_n,k) and the resulting G-sequence.

• Nonlinear Functional Analysis and Applications
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• v.29 no.1
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• pp.69-81
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• 2024

In this paper, we provide certain fixed point results for a generalized 𝛼-nonexpansive mapping, as well as a new iterative algorithm called SRJ-iteration for approximating the fixed point of this class of mappings in the setting of CAT(0) spaces. Furthermore, we establish strong and ∆-convergence theorem for generalized 𝛼-nonexpansive mapping in CAT(0) space. Finally, we present a numerical example to illustrate our main result and then display the efficiency of the proposed algorithm compared to different iterative algorithms in the literature. Our results obtained in this paper improve, extend and unify results of Abbas et al. [10], Thakur et al. [22] and Piri et al. [19].

• Journal of the Chungcheong Mathematical Society
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• v.19 no.3
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• pp.263-274
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• 2006

In this paper, we prove the Hyers-Ulam-Rassias stability of the quadratic mapping in generalized quasi-Banach spaces, and of the quadratic mapping in generalized p-Banach spaces.

• Genomics & Informatics
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• v.18 no.1
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• pp.2.1-2.11
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• 2020

In this paper, we propose a new approach to detecting outliers in a set of segmented genomes of the flu virus, a data set with a heterogeneous set of sequences. The approach has the following computational phases: feature extraction, which is a mapping into feature space, alignment-free distance measure to measure the distance between any two segmented genomes, and a mapping into distance space to analyze a quantum of distance values. The approach is implemented using supervised and unsupervised learning modes. The experiments show robustness in detecting outliers of the segmented genome of the flu virus.

• East Asian mathematical journal
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• v.24 no.1
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• pp.57-65
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• 2008

The approximate solvability of a generalized system for non-linear variational inequality in Hilbert spaces was studied, based on the convergence of projection methods. But little research was done in Banach space. The primary reason was that projection mapping lacked preferably property in Banach space. In this paper, we introduced the generalized projection methods. By using these methods, the results presented in this paper extended the main results of S. S. Chang [3] from Hilbert spaces to Banach space.

• Journal of the Korean Mathematical Society
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• v.41 no.1
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• pp.131-143
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• 2004

Let Ε and F be locally convex spaces over C. We assume that Ε is a nuclear space and F is a Banach space. Let f be a holomorphic mapping from Ε into F. Then we show that f is of uniformly bounded type if and only if, for an arbitrary locally convex space G containing Ε as a closed subspace, f can be extended to a holomorphic mapping from G into F.

• Korean Journal of Mathematics
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• v.9 no.2
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• pp.157-164
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• 2001

We construct an operad which is called the mapping class group operad. Its structure map is induced by the attachings of surfaces. The similar operad was constructed by Tillmann in order prove that ${\Gamma}^+_{\infty}$ is an infinite loop space. Our operad is rather simpler and easier to deal with.

• Proceedings of the IEEK Conference
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• 2002.07b
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• pp.924-927
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• 2002

In this paper we proposed the design space exploration environment of re-configurable hybrid systems and evaluate the performance by changing design parameters. With this, we analyzed the effect of various scheduling methods which determine how we allocate hardware/software resources to application program. A simple static (fixed) mapping strategy produces almost the same performance compared with a sophisticated dynamic mapping strategy especially when a CPU is already busy with its pre-assigned own tasks.

• Nonlinear Functional Analysis and Applications
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• v.26 no.3
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• pp.601-610
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• 2021

A convergence theorem for a generalized 𝜑-weakly contractive mapping is proved which satisfy a generalized contraction condition on a complete metrically convex metric space. The result in this paper generalizes the relevant results due to Rhoades [18], Alber and Guerre-Delabriere [1], Khan and Imdad [14], Xue [20] and others. An illustrative example is also furnished in support of our main result.

• Nonlinear Functional Analysis and Applications
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• v.26 no.5
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• pp.1105-1114
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• 2021

In this paper, we prove a fixed point theorem for G-contractive type non-self mapping in cone metric space endowed with a graph. Our result generalizes many results in the literature and provide a new pavement for solving nonlinear functional equations.