Invariant points under strict contractive conditions . Ravindra

This paper is intended to consider a new approach for obtaining common fixed points under strict contractive conditions in metric spaces without assuming continuity or completeness ( or closedness) of the range of any one of the involved maps. The results proved by us can be extended to the nonexpansive or Lipschitz type mapping pairs. Our results substantially improve the results of Pant [ Discontinuity and fixed points, J. Math. Anal. Appl. 240, (1999), 284-289], Imdad et al. [ Coincidence fixed points in symmetric spaces under strict contractions, J. Math. Anal. Appl. 320, (2006), 352-360], Jin-xuan and Yang [ Common fixed point theorems under strict contractive conditions in Menger spaces, Nonlinear Analysis 70, (2009), 184–193] and Pant and Pant [ Common fixed points under strict contractive conditions, J. Math. Anal. Appl. 248,(2000), 327-332]. Resumen. Este art́ıculo tiene la intención de considerar un nuevo enfoque para la obtención de puntos fijos comunes bajo estrictas condiciones contractivas en espacios métricos sin asumir la continuidad o integridad (o cercańıa) de la gama de cualquiera de los mapas implicados. Los resultados obtenidos por nosotros se puede extender a los mapas de tipo no expansivos o Lipschitz. Nuestros resultados mejoran sustancialmente los resultados de Pant [Discontinuity and fixed points, J. Math. Anal. Appl. 240, (1999), 284-289], Imdad et al. [ Coincidence fixed points in symmetric spaces under strict contractions, J. Math. Anal. Appl. 320, (2006), 352-360], Jin-xuan and Yang [ Common fixed point theorems under strict contractive conditions in Menger spaces, Nonlinear Analysis 70, (2009), 184–193] y Pant y Pant [ Common fixed points under strict contractive conditions, J. Math. Anal. Appl. 248,(2000), 327-332].