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

Abstract

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.

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“…The results of this research showed that the Caristi-Kirk fixed point in conical metric spaces turns into a result similar to traditional methods in reduced metric spaces. Bakery and Mohamed [4] proposed a new definition of the variable exponent of the Cesàro complex function space using the official power series. In this space, by utilizing s-numbers produced prequasi-ideal and then presented the topological and geometric structures of this class of ideal.…”