Common fixed point of generalized ($psi$-$varphi$)-weak contraction mappings

Abstract

Let (X; d) be a complete metric space and let f; g : X 􀀀! X betwo mappings which satisfy a ( 􀀀 ')-weak contraction condition or generalized( 􀀀 ')-weak contraction condition. Then f and g have a unique common xedpoint. Our results extend previous results given by Ciric (1971), Rhoades (2001),Branciari (2002), Rhoades (2003), Abbas and Ali Khan (2009), Zhang and Song(2009) and Moradi at. el. (2011).