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

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