... understudy, we have to check that Tx ≤ T(Tx) for all x Î X. For x = 4, we haveT4=4 T(T4)= T4=4. For x = 5, we haveT5=6 T(T5)= T6=4. For x = 6, we haveT6=4 T(T6)= T4=4.Thus, ... definition of ≤,wegetzn= zp=4foralln ≥ p. Thus, we have z = 4 and zn≤ z for alln ∈ N. Now, suppose that zn= 6 for alln∈ N. In this case, we get z = 6, andzn≤ z for alln∈ N. Thus, we ... common fixed point.A number of fixed point results may be obtained by assuming different forms for thefunctions ψ1and ψ2. In particular, fixed point results under various contractive condi-tions...