Some common fixed point theorems for a family of mappings in metrically convex spaces

Abstract

In the present paper some common fixed point theorems for a sequence and a pair of nonself-mappings in complete metrically convex metric spaces are proved which generalize such results due to Khan et al. [M.S. Khan, H.K. Pathak, M.D. Khan, Some fixed point theorems in metrically convex spaces, Georgian Math. J. 7 (3) (2000) 523–530], Assad [N.A. Assad, On a fixed point theorem of Kannan in Banach spaces, Tamkang J. Math. 7 (1976) 91–94], Chatterjea [S.K. Chatterjea, Fixed point theorems, C. R. Acad. Bulgare Sci. 25 (1972) 727–730] and several others. Some related results are also discussed.