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We have defined the variable exponent of the Cesàro complex function space of formal power series. We have constructed the prequasi-ideal generated by  s -numbers and this new space of complex functions. We present some topological and geometric structures of this class of ideal. The existence of Caristi’s fixed point is examined. Some geometric properties related to the fixed point theory are presented. Finally, real-world examples and applications show solutions to some nonlinear difference equations.

Fixed Point Property of Variable Exponent Cesàro Complex Function Space of Formal Power Series under Premodular