In this work, we establish new fixed point theorems for generalized Pata–Suzuki type contraction via α -admissible mapping in metric spaces and to prove some fixed point results for such mappings. Moreover, we give an example to illustrate our main result. Consequently, the results presented in this paper generalize and improve the corresponding results of the literature.

In this paper, we introduce concepts of generalized ( , ) − Geraghty contraction type mappings in modular metric spaces via ( , ) − admissible pair in modular metric spaces are essentially weaker than the class of − Geraghty contraction type mappings. We establish some fixed point and periodic point results for such contractions. Consequently, the obtained results encompass various generalizations of the Banach contraction principle.

In this paper, we give (α,φ)-weak Pata contractive mapping by using the simulation function and multivalued (α,φ)-weak Pata contractions and establish some fixed point results for such contractions. Also, we give an example related to (α,φ)-weak Pata contractive mappings via simulation function. Our results generalize some Pata-type contractions and Banach contractions. Consequently, the obtained results encompass several results in the literature.

In this work, we introduce weak Pata convex contractions and weak E -Pata convex contractions via simulation functions in metric spaces to prove some fixed point results for such mappings. Also, we consider an example related to weak Pata convex contractions. Consequently, our results generalize and unify some results in the literature.