PPF Dependent Fixed Point Results for Hybrid Rational and Suzuki-Edelstein Type Contractions in Banach Spaces

V. Parvaneh, H. Hosseinzadeh, N. Hussain, Lj. Ćirić

In this paper we introduce new notions of hybrid rational Geraghty and Suzuki--Edelstein type contractive mappings and investigate the existence and uniqueness of PPF dependent fixed point for such mappings in the Razumikhin class, where domain and range of the mappings are not the same. As an application of our PPF dependent fixed point results, we deduce corresponding PPF dependent coincidence point results in the Razumikhin class. Our results extend and improve the results of Sintunavarat and Kumam [J. Nonlinear Anal. Optim.: Theory Appl., Vol. 4, (2013), 157–162], Bernfeld, Lakshmikantham and Reddy [Applicable Anal., 6(1977), 271–280] and others. As an application of our results, we establish PPF dependent solution of a periodic boundary value problem.