• Communications of the Korean Mathematical Society
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• v.16 no.4
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• pp.607-619
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• 2001

Rassias obtained the Hyers-Ulam stability of the gen-eral Euler-Lagrange functional equation. In this paper we general-ized this stability in the spirit of Hyers, Ulam, Rassias and Gavruta.

• Honam Mathematical Journal
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• v.29 no.1
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• pp.61-74
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• 2007

Th. M. Rassias obtained the Hyers-Ulam stability of the general Euler-Lagrange functional equation. In this paper we prove the stability of generlized Euler-Lagrange functional equations in the spirit of Hyers, Ulam, Rassias and G$\breve{a}$vruta.

• Journal of applied mathematics & informatics
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• v.7 no.2
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• pp.693-701
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• 2000

In this paper, we investigate a generalization of the Ulam stability problem of the 3-dimensional Euler-Lagrange functional equation f(x-y-z)+f(x)+f( y)+f(z)= f(x-y) +f(y+z) +f(z-x)

• The Pure and Applied Mathematics
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• v.29 no.2
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• pp.189-199
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• 2022

In this paper, we introduce a new generalized (a, b)-cubic Euler-Lagrange-Jensen functional equation and obtain its general solution. Furthermore, we prove the Hyers-Ulam stability of the new generalized (a, b)-cubic Euler-Lagrange-Jensen functional equation in orthogonality normed spaces.

• Journal of the Chungcheong Mathematical Society
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• v.20 no.4
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• pp.535-542
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• 2007

In this paper, we investigate the generalized Hyers-Ulam{Rasssias stability of the following Euler-Lagrange type quadratic functional equation $$f(ax+by+cz)+f(ax+by-cz)+f(ax-by+cz)+f(ax-by-cz)=4a^2f(x)+4b^2f(y)+4c^2f(z)$$.

• Korean Journal of Mathematics
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• v.30 no.4
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• pp.571-592
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• 2022

By established a Banach space with the Hausdorff distance, we introduce the alternative fixed-point theorem to explore the existence and uniqueness of a fixed subset of Y and investigate the stability of set-valued Euler-Lagrange functional equations in this space. Some properties of the Hausdorff distance are furthermore explored by a short and simple way.

• Journal of the Chungcheong Mathematical Society
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• v.37 no.2
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• pp.87-97
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• 2024

For any fixed integers k, l with kl(l - 1) ≠ 0, we establish the generalized Hyers-Ulam stability of an Euler-Lagrange quadratic functional equation f(kx + ly) + f(kx - ly) + 2(l - 1)[k²f(x) - lf(y)] = l[f(kx + y) + f(kx - y)] in normed spaces and in non-Archimedean spaces, respectively.

• The Mathematical Education
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• v.22 no.3
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• pp.51-55
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• 1984

• Communications of the Korean Mathematical Society
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• v.28 no.2
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• pp.319-333
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• 2013

Using the fixed point method, we prove the generalized Hyers-Ulam-Rassias stability of the following functional equation in multi-Banach spaces: $${\sum_{1{\leq}i_<j{\leq}n}}\;f(\frac{r_ix_i+r_jx_j}{k})=\frac{n-1}{k}{\sum_{i=1}^n}r_if(x_i)$$.

• The Journal of Asian Finance, Economics and Business
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• v.8 no.11
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• pp.223-234
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• 2021

This study aims to examine whether operating cash flows influence banks' financial stability in Pakistan. The study employed annual panel data collected from annual reports of 20 commercial banks listed on the Pakistan Stock Exchange for the year 2011 to 2019. Free cash flow yield was taken as the dependent variable while cash flow ratio was selected as the independent variable, and net interest margin, income diversification, asset quality, financial leverage, the cost to income ratio, advance net of provisions to total assets ratio, capital ratio, financial performance, breakup value per share and bank size were taken as control variables. The study performed ordinary least square technique, random and fixed effects models, Hausman test, Lagrange multiplier test, descriptive and correlation analysis. Results showed that operating cash flows and net interest margin significantly and positively influenced banks' financial stability while the cost to income ratio and advances net of provisions to total assets ratio significantly and negatively associated with banks' financial stability. To improve financial stability, banks should become more cost-effective and enhance their liquidity levels by lowering lending activities. In the future, it would be useful to compare commercial and investment banks, also Islamic and conventional banks in the same research setting.