A Generalization of Caristi's Fixed Point Theorem in the Variable Exponent Weighted Formal Power Series Space

Abstract

Suppose pn be sequence of positive reals. By Hwpn, we represent the space of all formal power series ∑n=0∞anzn equipped with ∑n=0∞λan/n+1pn<∞, for some λ>0. Various topological and geometric behavior of Hwpn and the prequasi ideal constructs by s-numbers and Hwpn have been considered. The upper bounds for s-numbers of infinite series of the weighted n-th power forward shift operator on Hwpn with applications to some entire functions are granted. Moreover, we investigate an extrapolation of Caristi's fixed point theorem in Hwpn.