Value cross-sharing problems on meromorphic functions

In this paper, we continue to consider the value cross-sharing problems on meromorphic functions. We mainly present some results and improvements on \(f(z)\) and \(g(z)\) provided that \(f(z)\) and \(g^{(k)}(z)\) share common values together with \(g(z)\) and \(f^{(k)}(z)\) share the same or different common values CM or IM, where \(f(z), g(z)\) are meromorphic functions and \(k\) is a positive integer. With additional conditions on deficiency, we get more accurate relations on \(f(z)\) and \(g(z)\) when \(f(z)\) and \(g^{(k)}(z)\) share a CM together with \(g(z)\) and \(f^{(k)}(z)\) share b CM, where a, b are constants.