PPF DEPENDENT FIXED POINT THEOREMS FOR RATIONAL TYPE CONTRACTION MAPPINGS IN BANACH SPACES - Sintunavarat, W.; Kumam, P. (Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO), 2013)
In this paper, we prove the existence of the PPF dependent fixed point theorems in the Razumikhin class for rational type contraction mappings in Banach spaces where the domain and range of the mappings are not the same. We also use this result to prove the PPF dependent coincidence point theorems. Our results extend and generalize some results of Bernfeld et al. in [S. R. Bernfeld, V. Lakshmikatham and Y. M. Reddy, Fixed point theorems of operators with PPF dependence in Banach spaces, Applicable Anal. 6 (1977), 271-280.].