Fixed point results for $(\zeta , \eta )$-weakly cyclic generalized contraction mappings in b-metric spaces

The present study introduces $(\zeta , \eta )$ -weakly cyclic generalized contraction mappings in the context of b-metric spaces and investigates results of fixed-point for it. Our findings extend and generalize a large number of relevant fixed-point results from the current literature. Examples are provided to support the validity of our findings. Finally, we apply our findings to demonstrate the existence and uniqueness of a solution for a non-linear Fredholm integral equation.