Fixed point theorems of three mappings with new functional inequality (Q1064575)

Common fixed point theorems of three maps f,g and h from a complete metric space (X,d) into itself are proved. The maps f,g and h satisfy \[ [d(fx,gy)]^ 2\leq \phi [d(hx,fx)d(hy,gy),d(hx,gy)d(hy,fx),d(hx,fx)d(hx,gy),d(hy,fx)d(hy,gy)] \] for all x,y\(\in X\), and \(fh=hf\), \(gh=hg\), f(X)\(\subset h(X)\) and g(X)\(\subset h(X)\) where \(\phi\) is an upper semi-continuous function from \(R^{+4}\) to \(R^+\), satisfying: \(\phi (t,t,a_ 1t,a_ 2t)<t\) for any \(t>0\) and \(a_ i\in \{0,1,2\}\) such that \(a_ 1+a_ 2=2\).