• Korean Journal of Mathematics
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• 제14권1호
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• pp.79-83
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• 2006

In this paper, we apply Zermelo's problem of navigation on Riemannian manifolds to Hermitian manifolds. Using a similar technique with which we define a Randers metric in a Finsler manifold by perturbing Riemannian metric with a vector field, we construct an $(a,b,f)$-metric in a Rizza manifold from a Hermitian metric and a given vector field.

• Nonlinear Functional Analysis and Applications
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• 제28권4호
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• pp.1087-1095
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• 2023

In this paper, the concept of a weighted b_ν(α)-metric space is introduced as a generalization of the b_ν(s)-metric space and ν-metric space. We prove some fixed point results of the Reich-type contraction in the weighted b_ν(α)-metric space. Furthermore, we generalize Reich's theorem by extending the result to a weighted b_ν(α)-metric space.

• East Asian mathematical journal
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• 제32권5호
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• pp.677-684
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• 2016

In this paper, the notion of S-metric spaces will be introduced. We present some fixed point theorems for two maps on complete S-metric spaces and an illustrative example is given for the single-valued case. By using the similar method as in [4], a common fixed point theorem for two single-valued mappings is obtained in S-metric spaces.

• 충청수학회지
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• 제23권4호
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• pp.645-656
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• 2010

In this paper, we prove a common fixed point theorem for four mappings on fuzzy 2-metric spaces. Our result is an extension of results of S. H. Cho [2] to fuzzy 2-metric spaces. Also, it is a generalization of a result of S. Sharma [11].

• 한국국방경영분석학회지
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• 제22권2호
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• pp.90-112
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• 1996

Research issues in software engineering in recent may be object oriented methodology and software quality. Since Halstead has proposed metric-software science in 1977, software quality area has been studied in steady but inactively until 1980s. As international standards such as ISO 9000-3, 9126 were enacted in 1990s early, interest in software quality is increased but many problems such as how to validate metric, measure quality or apply metric are remained. This paper proposes software quality metric methodology which software developer or project manager can use in measuring quality and validating metric during software development. The methodology is classified by several phases: establishment of quality requirement, identification of quality metric, data collection, metric implementation, metric validation. In order to show its applicability, test program, metrics and data are applied to each phase of the methodology. Consideration of this methodology as a methodology for software quality measurement similar to development methodology for software development is needed.

• 대한수학회논문집
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• 제35권1호
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• pp.185-199
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• 2020

In this paper, we introduce the definitions of s_p-convergent sequence in fuzzy metric spaces and fuzzy normed spaces. We investigate relations of convergence, s_p-convergence, s_∞-convergence and st-convergence in fuzzy metric spaces and fuzzy normed spaces. We also study s_p-convergence, s_∞-convergence and st-convergence using the sub-sequence of convergent sequence in fuzzy metric spaces and fuzzy normed spaces. Stationary fuzzy normed spaces are defined and investigated. We finally define s_p-closed sets, s_∞-closed sets and st-closed sets in fuzzy metric spaces and fuzzy normed spaces and investigate relations of them.

• Nonlinear Functional Analysis and Applications
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• 제28권2호
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• pp.571-587
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• 2023

In this paper, we have developed the idea of α-β-ψ-contractive mapping in S-metric space and renamed it α_s-β_s-ψ-contractive mapping. We have proved some results of fixed point present in literature in partially ordered S-metric space using α_s-β_s-admissible and α_s-β_s-ψ-contractive mapping.

• Nonlinear Functional Analysis and Applications
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• 제29권3호
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• pp.635-648
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• 2024

In this paper, we extend the concept of S-contractions of type E in an S-metric space. Further, by combining simulation function and S-contractions of type E, we examine the existence and uniqueness of fixed point in a complete S-metric space. Sufficient examples are provided and application to the solution of integral equation is also made.

• Journal of applied mathematics & informatics
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• 제40권3_4호
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• pp.669-674
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• 2022

In this paper, we shall consider some properties of the metric projection as a set valued mapping. For a set G in a metric space E, the mapping 𝜋_G; x → 𝜋_G(x) of E into 2^G is called set valued metric projection of E onto G. We investigated the properties related to the projection P_S(·)(·) and 𝜋_S(·)(·) as one-sided best simultaneous approximations.

• Structural Engineering and Mechanics
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• 제17권6호
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• pp.767-788
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• 2004

The classical 8-node isoparametric serendipity element uses parametric shape functions for both test and trial functions. Although this element performs well in general, it yields poor results under severe mesh distortions. The distortion sensitivity is caused by the lack of continuity and/or completeness of shape functions used for test and trial functions. A recent element using parametric and metric shape functions for constructing the test and trial functions exhibits distortion immunity. This paper discusses the choice of parametric or metric shape functions as the basis for test and/or trial functions, satisfaction of continuity and completeness requirements, and their connection to distortion sensitivity. Also, the performances of four types of elements, viz., parametric, metric, parametric-metric, and metric-parametric, are compared for distorted meshes, and their merits and demerits are discussed.