• 제목/요약/키워드: Quasi norm

검색결과 22건 처리시간 0.02초

STABILITY OF THE MONOMIAL FUNCTIONAL EQUATION IN QUASI NORMED SPACES

  • Mirmostafaee, Alireza Kamel
    • 대한수학회보
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    • 제47권4호
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    • pp.777-785
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    • 2010
  • Let X be a linear space and Y be a complete quasi p-norm space. We will show that for each function f : X $\rightarrow$ Y, which satisfies the inequality ${\parallel}{\Delta}_x^nf(y)\;-\;n!f(x){\parallel}\;{\leq}\;\varphi(x,y)$ for suitable control function $\varphi$, there is a unique monomial function M of degree n which is a good approximation for f in such a way that the continuity of $t\;{\mapsto}\;f(tx)$ and $t\;{\mapsto}\;\varphi(tx,\;ty)$ imply the continuity of $t\;{\mapsto}\;M(tx)$.

A Fixed Point Approach to the Stability of Quadratic Equations in Quasi Normed Spaces

  • Mirmostafaee, Alireza Kamel
    • Kyungpook Mathematical Journal
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    • 제49권4호
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    • pp.691-700
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    • 2009
  • We use the fixed alternative theorem to establish Hyers-Ulam-Rassias stability of the quadratic functional equation where functions map a linear space into a complete quasi p-normed space. Moreover, we will show that the continuity behavior of an approximately quadratic mapping, which is controlled by a suitable continuous function, implies the continuity of a unique quadratic function, which is a good approximation to the mapping. We also give a few applications of our results in some special cases.

Fuzzy Relations and Metrics

  • Kim, Yong-Chan;Kim, Young-Sun
    • International Journal of Fuzzy Logic and Intelligent Systems
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    • 제9권1호
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    • pp.30-35
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    • 2009
  • We investigate the properties of fuzzy relations, metrics and $\bigodot$-equivalence relation on a stsc quantale lattice L and a commutative cqm-lattice. In particular, pseudo-(quasi-) metrics induce $\bigodot$-(quasi)-equivalence relations.

DEGREE OF APPROXIMATION BY KANTOROVICH-CHOQUET QUASI-INTERPOLATION NEURAL NETWORK OPERATORS REVISITED

  • GEORGE A., ANASTASSIOU
    • Journal of Applied and Pure Mathematics
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    • 제4권5_6호
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    • pp.269-286
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    • 2022
  • In this article we exhibit univariate and multivariate quantitative approximation by Kantorovich-Choquet type quasi-interpolation neural network operators with respect to supremum norm. This is done with rates using the first univariate and multivariate moduli of continuity. We approximate continuous and bounded functions on ℝN , N ∈ ℕ. When they are also uniformly continuous we have pointwise and uniform convergences. Our activation functions are induced by the arctangent, algebraic, Gudermannian and generalized symmetrical sigmoid functions.

FIXED POINT THEOREM ON SOME ORDERED METRIC SPACES AND ITS APPLICATION

  • CHANG HYEOB SHIN
    • Journal of applied mathematics & informatics
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    • 제42권1호
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    • pp.93-104
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    • 2024
  • In this paper, we will prove a fixed point theorem for self-mappings on a generalized quasi-ordered metric space which is a generalization of the concept of a generalized metric space with a partial order and we investigate a genralized quasi-ordered metric space related with fuzzy normed spaces. Further, we prove the stability of some functional equations in fuzzy normed spaces as an application of our fixed point theorem.

Selection of Energy Conservation Measures for Building Energy Retrofit: a Comparison between Quasi-steady State and Dynamic Simulations in the Hands of Users

  • Kim, Sean Hay
    • KIEAE Journal
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    • 제16권6호
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    • pp.5-12
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    • 2016
  • Purpose: Quasi-steady state simulations have played a pivoting role to expand the user group of simulation to design engineers and architects in Korea. Initially they are introduced in the market as a building energy performance rating tool. In domestic practice, however, quasi-steady state simulations seem to be regarded as a de facto simulation only available for energy retrofit. Selection of ECMs and economic feasibility analysis are being decided through these tools, which implies that running these tools has become a norm step of the Investment-grade Audit. Method: This study aims at identifying issues and problems with the current practice via test cases, analyzing the reasons and opportunities, and then eventually suggesting proper uses of quasi-steady state and dynamic simulations. Result: The functionality of quasi-steady state simulations is more optimized to the rating. If they are to used for energy retrofits, their off-the-shelf functions also need to be expanded for customization and detailed reports. Yet their roles may be limited only to the go/no go decision; because their algorithms are still weak at precisely estimating energy and load savings that are required for making investment decisions compared to detailed simulations.