Stability of the generalized quadratic and quartic type functional equation in non-Archimedean fuzzy normed spaces |
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Authors: | Zhihua Wang and Prasanna K. Sahoo |
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Affiliation: | School of Science, Hubei University of Technology, Wuhan, Hubei 430068, China and Department of Mathematics, University of Louisville, Louisville, KY 40292, USA |
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Abstract: | In this paper, we prove some stability results concerning the generalized quadratic and quartic type functional equation in the context of non-Archimedean 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. |
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Keywords: | Fuzzy stability fuzzy norm non-Archimedean fuzzy normed space quadratic and quartic type functional equation. |
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