On an extension of a global implicit function theorem

We study the existence of global implicit functions for equations defined on open subsets Banach spaces. The partial derivative with respect to second variable is only required have a left inverse instead being invertible. Generalizing known results, we provide sufficient criteria which are easy check. These conditions essentially rely diffeomorphisms between respective projections set zeros and appropriate spaces, as well corresponding growth bound. further allow consider cases where function not all subset first variable.