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

Vahid Parvaneh, Hasan Hosseinzadeh, Nawab Hussain, Ljubomir Ciric


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 result, we establish
PPF dependent solution of a periodic boundary value problem.

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