Bohr's phenomenon for holomorphic and harmonic functions with lacunary series in complex Banach spaces.

We determine the sharp Bohr inequality for holomorphic functions defined on a balanced domain G of a complex Banach space X and takes values from the unit disk. Also, we investigate the Bohr-type inequalities for harmonic functions $ f=h+\bar {g} $ f = h + g ¯ defined on a balanced domain $ G\subset X $ G ⊂ X. [ABSTRACT FROM AUTHOR]