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September 10, 2025Open Access

Fixed point of generalized F-Suzuki contraction mapping on complete extended b-metric spaces with application

Key Points

Generalized F-Suzuki contractions establish fixed point results, extending existing theories in the field.
The findings prove fixed point theorems that unify and generalize many previous results in b-metric spaces.
The application of these results is demonstrated in solving Fredholm integral equations effectively.
The methods employed provide a foundation for further research on contraction mappings and their applications.

Abstract

The present article introduces the concept of generalized F-Suzuki type contraction in the setting of extended b-metric spaces, inspired by the existing concept in b-metric spaces. The newly introduced notion is further utilized to prove fixed point theorems for F-Suzuki type contraction which unified, extended and generalized many existing results in the literature. Finally, the established results are utilized to solve Fredholm integral equation.

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