Objectives In this paper we introduce fixed point theorems for generalized rational type $$\alpha$$ α -admissible contractive mappings in partially ordered b-metric spaces and prove the existence and uniqueness of fixed points for self-mappings satisfying the established theorems. Finally, we provide examples in support of our main findings in the setting of partially ordered b-metric spaces. Result New fixed point results have been obtained for generalized rational type $$\alpha$$ α -admissible contractive mappings in the setting of partially ordered b-metric space and we applied one of our results to determine a solution to an integral equation.

The purpose of this paper is to establish new type of fixed point result for a single self-mapping in the setting of dislocated quasi-metric space. Our established result generalizes and modifies some existing fixed point theorems in the literature. Appropriate example for the usability of the established result is also given.

In this paper, we introduce generalized α , ψ -contraction mappings in the setting of rectangular b -metric spaces and established existence and uniqueness of fixed points for the mappings introduced. Our results extend and generalize related fixed point results in the existing literature. We derive some consequences and corollaries from our obtained results. Also, we provide examples in support of our main findings. Furthermore, we determined a solution to an integral equation by applying our obtained results.

In this paper, we introduce the class of rectangular quasi b-metric spaces as a generalization of rectangular metric spaces, rectangular quasi-metric spaces, rectangular b-metric spaces, define generalized $(\alpha ,\psi ) $ ( α , ψ ) -contraction mappings and study fixed point results for the maps introduced in the setting of rectangular quasi b-metric spaces. Our results extend and generalize related fixed point results in the literature, in particular, the works of Karapinar and Lakzian (J. Funct. Spaces 2014:914398, 2014), Alharbi et al. (J. Math. Anal. 9(3):47–60, 2018), and Khuangsatung et al. (Thai J. Math. 2020:89–101, 2020) from rectangular quasi metric space and rectangular b-metric space to rectangular quasi b-metric spaces. We also provide examples in support of our main findings. Furthermore, we applied one of our results to determine the existence of a solution to an integral equation.

In this paper, we introduce an almost generalized α -admissible Z -contraction with the help of a simulation function and study fixed point results in the setting of partially ordered b-metric spaces. The presented results generalize and unify several related fixed point results in the existing literature. Finally, we verify our results by using two examples. Moreover, one of our fixed point results is applied to guarantee the existence of a solution of an integral equation.