Summary: We use the generalized Lipschitzian condition as employed by M. Imdad and A. H. Soliman [Fixed Point Theory Appl. 2010, Article ID 692401, 14 p. (2010; Zbl 1208.54016)] to extend the Lipschitzian condition which was used on the common fixed point theorems for one parameter semigroups of asymptotically regular mappings in Banach spaces by several authors before. Our results extend some relevant common fixed point theorems due to the works of J. Górnicki [Rend. Circ. Mat. Palermo (2) 46, No. 1, 89–118 (1997; Zbl 0889.47030)] and A. Wiśnicki [J. Math. Anal. Appl. 393, No. 1, 177–184 (2012; Zbl 1263.47072)].