PPF Dependent Fixed Points of Generalized Weakly Contraction Maps Via $c_g-$simulation Functions

Year 2019, Volume: 1 Issue: 2, 66 - 88, 30.10.2019

G. V. R. Babu , Madugula Vinod Kumar

Abstract

In this paper, we introduce the notion of generalized weakly  $Z_{G,\alpha,\mu,\xi,\eta,\varphi}-$contraction maps with respect to the $C_G-$simulation function and prove the existence of  PPF dependent fixed points of nonself maps in Banach spaces. For such maps, PPF dependent fixed points may not be unique. We provide an example  to illustrate this phenomenon.

Keywords

\alpha-admissible, \mu-subadmissible, C-class function, Razumikhin class, PPF dependent fixed point, simulation function, C_G-simulation function

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