We give a neccesary and sufficient condition on a function？such that the composition operator (Nemytskij Operator) H defined by acts in the space and satisfies a local Lipschitz condition. And, we prove that every locally defined operator mapping the space of continuous and bounded Wiener p(·)-variation with variable exponent functions into itself is a Nemytskij com-position operator.
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such that the composition operator (Nemytskij Operator) H defined by ![\"\"](\"Edit_19bc3ee9-3feb-4ea9-819b-362a0335af8d.bmp\")
acts in the space![\"\"](\"Edit_c1b352f8-dd17-47fc-a4d9-f1197d517a42.bmp\")
and satisfies a local Lipschitz condition. And, we prove that every locally defined operator mapping the space of continuous and bounded Wiener p(
