STABILITY OF THE GENERALIZED QUADRATIC AND QUARTIC TYPE FUNCTIONAL EQUATION IN NON-ARCHIMEDEAN FUZZY NORMED SPACES

Zhihua Wang; Prasanna K. Sahoo

doi:10.11948/2016060

2016 Volume 6 Issue 4

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Zhihua Wang, Prasanna K. Sahoo. STABILITY OF THE GENERALIZED QUADRATIC AND QUARTIC TYPE FUNCTIONAL EQUATION IN NON-ARCHIMEDEAN FUZZY NORMED SPACES[J]. Journal of Applied Analysis & Computation, 2016, 6(4): 917-938. doi: 10.11948/2016060

Citation:

Zhihua Wang, Prasanna K. Sahoo. STABILITY OF THE GENERALIZED QUADRATIC AND QUARTIC TYPE FUNCTIONAL EQUATION IN NON-ARCHIMEDEAN FUZZY NORMED SPACES[J]. Journal of Applied Analysis & Computation, 2016, 6(4): 917-938. doi: 10.11948/2016060

STABILITY OF THE GENERALIZED QUADRATIC AND QUARTIC TYPE FUNCTIONAL EQUATION IN NON-ARCHIMEDEAN FUZZY NORMED SPACES

1 School of Science, Hubei University of Technology, Wuhan, Hubei 430068, China;
2 Department of Mathematics, University of Louisville, Louisville, KY 40292, USA

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Abstract

Abstract

In this paper, we prove some stability results concerning the generalized quadratic and quartic type functional equation in the context of nonArchimedean fuzzy normed spaces in the spirit of Hyers-Ulam-Rassias. As applications, we establish some results of approximately generalized quadratic and quartic type mapping in non-Archimedean normed spaces. Also, we show that the assumption of the non-Archimedean absolute value of 2 is less than 1 cannot be omitted in our corollaries. The results improve and extend some recent results.
- Fuzzy stability /
- fuzzy norm /
- non-Archimedean fuzzy normed space /
- quadratic and quartic type functional equation
MSC: 39B82;39B72

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