Some new cyclic admissibility type with uni-dimensional and multidimensional fixed point theorems and its applications

In this paper, we introduce the concept of a cyclic ( α , β ) -admissible mapping type S and the notion of an ( α , β ) - ( ψ , φ ) -contraction type S . We also establish fixed point results for such contractions along with the cyclic ( α , β ) -admissibility type S in complete b -metric spaces and provide some examples for supporting our result. Applying our new results, we obtain fixed point results for cyclic mappings and multidimensional fixed point results. As application, the existence of a solution of the nonlinear integral equation is discussed.