| Summary: | In this paper, we introduce $ \mathcal{J}_{s; \Omega} $-families of generalized pseudo-$ b $-distances in $ b $-gauge spaces $ (U, {Q}_{s; \Omega}) $. Moreover, by using these $ \mathcal{J}_{s; \Omega} $-families on $ U $, we define the $ \mathcal{J}_{s; \Omega} $-sequential completeness and construct an $ F $-type contraction $ T:U\rightarrow U $. Furthermore, we develop novel periodic and fixed point results for these mappings in the setting of $ b $-gauge spaces using $ \mathcal{J}_{s; \Omega} $-families on $ U $, which generalize and improve some of the results in the corresponding literature. The validity and importance of our theorems are shown through an application via an existence solution of an integral equation.
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