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

Document Type : Research Paper

Authors
Department of Mathematics, Faculty of Science, Arak University, Arak, 38156- 8-8349, Iran.
Abstract
Let $(X, d)$ be a complete metric space and let $f,g : X \to X$ be two mappings which satisfy a ($\psi$-$\varphi$)-weak contraction condition or generalized ($\psi$-$\varphi$)-weak contraction condition. Then $f$ and $g$ have a unique common fixed point. 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).
Keywords

  • Receive Date 09 June 2011
  • Revise Date 11 June 2012
  • Accept Date 25 June 2012

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