Generalized $ \alpha $-$ \psi $-Geraghty contraction type fixed point theorems in strong $ b $-metric spaces

This paper aims to present the new concept of generalized $ \alpha $-$ \psi $-Geraghty contraction type for both single-valued and multi-valued mappings in a strong $ b $-metric space. Our approach extends the concepts introduced by Karapınar for single-valued mappings and by Afshari et al. for multi-valued mappings. Several results on the fixed point theory of this contraction type are provided both globally (in the entire space) and locally (in the closed ball). Our findings expand and enhance several fixed point theorems, including the famous Geraghty's theorem. Examples and an application of integral equations are included to illustrate these results.