Fixed point theorems for asymptotically regular semigroups equipped with generalized Lipschitzian conditions in metric spaces

Abstract

In this paper, we prove some common fixed point theorems for one-parameter semigroups of asymptotically regular mappings which satisfy certain generalized Lipschitzian conditions in metric spaces. Our results do not assume the continuity of the mappings in the semigroups. The results extend some relevant common fixed point theorems in Gornicki (Colloq Math 64:55–57, 1993), Imdad and Soliman (Fixed Point Theory Appl 2010:692401, 2010), Imdad and Soliman (Bull Malays Math Sci Soc 2(35):687–694, 2012), Yao and Zeng (J Nonlinear Convex Anal 8:153–163, 2007).