• Title/Summary/Keyword: fuzzy Banach spaces

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HYERS-ULAM STABILITY OF DERIVATIONS IN FUZZY BANACH SPACE: REVISITED

  • Lu, Gang;Jin, Yuanfeng;Wu, Gang;Yun, Sungsik
    • The Pure and Applied Mathematics
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    • v.25 no.2
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    • pp.135-147
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    • 2018
  • Lu et al. [27] defined derivations on fuzzy Banach spaces and fuzzy Lie Banach spaces and proved the Hyers-Ulam stability of derivations on fuzzy Banach spaces and fuzzy Lie Banach spaces. It is easy to show that the definitions of derivations on fuzzy Banach spaces and fuzzy Lie Banach spaces are wrong and so the results of [27] are wrong. Moreover, there are a lot of seroius problems in the statements and the proofs of the results in Sections 2 and 3. In this paper, we correct the definitions of biderivations on fuzzy Banach algebras and fuzzy Lie Banach algebras and the statements of the results in [27], and prove the corrected theorems.

ON THE DEBREU INTEGRAL OF FUZZY MAPPINGS IN BANACH SPACES

  • Park, Chun-Kee
    • The Pure and Applied Mathematics
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    • v.16 no.3
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    • pp.315-326
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    • 2009
  • In this paper, we introduce Debreu integral of fuzzy mappings in Banach spaces in terms of the Debreu integral of set-valued mappings, investigate properties of Debreu integral of fuzzy mappings in Banach spaces and obtain the convergence theorem for Debreu integral of fuzzy mappings in Banach spaces.

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ON THE PETTIS INTEGRAL OF FUZZY MAPPINGS IN BANACH SPACES

  • Park, Chun-Kee
    • Communications of the Korean Mathematical Society
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    • v.22 no.4
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    • pp.535-545
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    • 2007
  • In this paper, we introduce the Pettis integral of fuzzy mappings in Banach spaces using the Pettis integral of closed set-valued mappings. We investigate the relations between the Pettis integral, weak integral and integral of fuzzy mappings in Banach spaces and obtain some properties of the Pettis integral of fuzzy mappings in Banach spaces.

SOME RESULTS ON FUZZY BANACH SPACES

  • SAADATI R.;VAEZPOUR S. M.
    • Journal of applied mathematics & informatics
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    • v.17 no.1_2_3
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    • pp.475-484
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    • 2005
  • The main aim of this paper is to consider the fuzzy norm, define the fuzzy Banach spaces, its quotients and prove some theoremes and in particular Open mapping and Closed graph theoremes on these spaces.

FUZZY NONLINEAR RANDOM VARIATIONAL INCLUSION PROBLEMS INVOLVING ORDERED RME-MULTIVALUED MAPPING IN BANACH SPACES

  • Kim, Jong Kyu;Salahuddin, Salahuddin
    • East Asian mathematical journal
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    • v.34 no.1
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    • pp.47-58
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    • 2018
  • In this paper, we consider a fuzzy nonlinear random variational inclusion problems involving ordered RME-multivalued mapping in ordered Banach spaces. By using the random relaxed resolvent operator and its properties, we suggest an random iterative algorithm. Finally both the existence of the random solution of the original problem and the convergence of the random iterative sequences generated by random algorithm are proved.

FUZZY GENERAL NONLINEAR ORDERED RANDOM VARIATIONAL INEQUALITIES IN ORDERED BANACH SPACES

  • Salahuddin, Salahuddin;Lee, Byung-Soo
    • East Asian mathematical journal
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    • v.32 no.5
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    • pp.685-700
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    • 2016
  • The main object of this work to introduced and studied a new class of fuzzy general nonlinear ordered random variational inequalities in ordered Banach spaces. By using the random B-restricted accretive mapping with measurable mappings ${\alpha},{\alpha}^{\prime}:{\Omega}{\rightarrow}(0,1)$, an existence of random solutions for this class of fuzzy general nonlinear ordered random variational inequality (equation) with fuzzy mappings is established, a random approximation algorithm is suggested for fuzzy mappings, and the relation between the first value $x_0(t)$ and the random solutions of fuzzy general nonlinear ordered random variational inequality is discussed.

ON HENSTOCK INTEGRAL OF FUZZY MAPPINGS IN BANACH SPACES

  • Oh, Mee Na;Park, Chun-Kee
    • Korean Journal of Mathematics
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    • v.17 no.3
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    • pp.257-270
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    • 2009
  • In this paper we introduce the Henstock integral of fuzzy mappings in Banach spaces as a generalization of the Henstock integral of set-valued mappings and investigate some properties of it.

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EXTENSIONS OF BANACH'S AND KANNAN'S RESULTS IN FUZZY METRIC SPACES

  • Choudhur, Binayak S.;Das, Krishnapada;Das, Pradyut
    • Communications of the Korean Mathematical Society
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    • v.27 no.2
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    • pp.265-277
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    • 2012
  • In this paper we establish two common fixed point theorems in fuzzy metric spaces. These theorems are generalisations of the Banach contraction mapping principle and the Kannan's fixed point theorem respectively in fuzzy metric spaces. Our result is also supported by examples.

CONVERGENCE THEOREM FOR KURZWEIL-HENSTOCK-PETTIS INTEGRABLE FUZZY MAPPINGS

  • Park, Chun-Kee
    • Journal of the Chungcheong Mathematical Society
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    • v.23 no.2
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    • pp.279-291
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    • 2010
  • In this paper, we introduce the Kurzweil-Henstock-Pettis integral of fuzzy mappings in Banach spaces in terms of the Kurzweil-Henstock-Pettis integral of set-valued mappings and obtain some properties of the Kurzweil-Henstock-Pettis integral of fuzzy mappings in Banach spaces and the convergence theorem for Kurzweil-Henstock-Pettis integrable fuzzy mappings.