"In this work, we prove the Hyers–Ulam stability of hom-derivations in complex Banach algebras, associated with the additive $(s_{1}, s_{2})$-functional inequality: \begin{eqnarray}\label{0.1} \nonumber \| f(a+b) - f(a) - f(b)\| &\le& \left \|s_{1} \left(f(a+b) + f(a-b)-2f(a)\right)\right\| \\ &\quad& + \left \|s_{2} \left(2f\left( \frac{a+b}{2}\right) - f(a) - f(b)\right)\right\|, \end{eqnarray} where $s_{1}$ and $s_{2}$ are fixed nonzero complex numbers with $\sqrt{2}|s_{1}|+|s_{2}| < 1$."
In this paper, we construct a new parallel method to solve common variational inclusion and common fixed point problems in a real Hilbert space. We obtain a weak convergence theorem by using this method. Besides, numerical results on the signal recovery problem consisting of various blurred filters present that our proposed method outperforms the two previous methods.
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