HYPERSTABILITY RESULTS FOR GENERALIZED QUADRATIC FUNCTIONAL EQUATIONS IN $(2,\alpha)$-BANACH SPACES

Iz-iddine EL-Fassi; El-sayed El-hady; Wutiphol Sintunavarat

doi:10.11948/20220462

2023 Volume 13 Issue 5

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Article navigation > Journal of Applied Analysis & Computation > 2023 > 13(5): 2596-2612

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Iz-iddine EL-Fassi, El-sayed El-hady, Wutiphol Sintunavarat. HYPERSTABILITY RESULTS FOR GENERALIZED QUADRATIC FUNCTIONAL EQUATIONS IN $(2,\alpha)$-BANACH SPACES[J]. Journal of Applied Analysis & Computation, 2023, 13(5): 2596-2612. doi: 10.11948/20220462

Citation:

Iz-iddine EL-Fassi, El-sayed El-hady, Wutiphol Sintunavarat. HYPERSTABILITY RESULTS FOR GENERALIZED QUADRATIC FUNCTIONAL EQUATIONS IN $(2,\alpha)$-BANACH SPACES[J]. Journal of Applied Analysis & Computation, 2023, 13(5): 2596-2612. doi: 10.11948/20220462

HYPERSTABILITY RESULTS FOR GENERALIZED QUADRATIC FUNCTIONAL EQUATIONS IN $(2,\alpha)$-BANACH SPACES

1.
Department of Mathematics, Faculty of Sciences and Techniques, Sidi Mohamed Ben Abdellah University, B.P. 2202, Fez, Morocco
2.
Mathematics Department, College of Science, Jouf University, P.O. Box: 2014, Sakaka, Saudi Arabia
3.
Basic Science Department, Faculty of Computers and Informatics, Suez Canal University, Ismailia, 41522, Egypt
4.
Thammasat University Research Unit in Fixed Points and Optimization, Thammasat University Rangsit Center, 12120, Pathum Thani, Thailand
5.
Department of Mathematics and Statistics, Faculty of Science and Technology, Thammasat University Rangsit Center, 12120, Pathum Thani, Thailand

Author Bio: Email: iziddine.elfassi@usmba.ac.ma(Iz. EL-Fassi); Email: elsayed_elhady@ci.suez.edu.eg(El. El-hady)
Corresponding author: Email: wutiphol@mathstat.sci.tu.ac.th (W. Sintunavarat)

Abstract

Abstract

In this article, we utilize a special version of some recent fixed point theorem to investigate the hyperstability of the following generalized quadratic functional equation with $F$ is the unknown function from a special subset $X$ of a (2, $\beta$)-normed space over the field $\mathbb{F}$ into a (2, $\alpha$)-Banach space over the field $\mathbb{K}$:
$F(ax_1+bx_2)+F(cx_1+dx_2)=rF(x_1)+sF(x_2)$
for all $x_1, x_2 \in X$, where $a, b, c, d\in \mathbb{F}$ and $r, s\in \mathbb{K}$. In this way, we generalize several earlier outcomes.
- Functional equations /
- hyperstability /
- fixed point theory
MSC: 97I70, 37C25, 39B52, 39B8

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References

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