In this paper, we introduce the concept of generalized orthogonal F -Suzuki contraction mapping and prove some fixed point theorems on orthogonal b -metric spaces. Our results generalize and extend some of the well-known results in the existing literature. As an application of our results, we show the existence of a unique solution of the first-order ordinary differential equation.

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The notion of symmetry is the main property of a metric function. The area of fixed point theory has a suitable structure for symmetry in mathematics. The goal of this paper is to find fixed point and common fixed point results in a bicomplex valued b-metric space for mixed type rational contractions with control functions. Some well-known literature findings were generalized in our main findings. We provide an example to strengthen and validate our main results. As an example, in the context of bicomplex-valued b-metric space, we develop fixed point and common fixed point results for the rational contraction mapping.

In this paper, we introduce orthogonal concepts concerning F -contraction mappings and demonstrate some fixed-point theorems for self-mapping in a complete orthogonal metric space. Some well-known results in the literature are generalized and modified based on the demonstrated results. An example is provided to support our results, which are used in an application.

<abstract><p>In the present paper, we introduce the notion of a $ \mathcal{C}^{\star} $-algebra valued bipolar metric space and prove coupled fixed point theorems. Some of the well-known outcomes in the literature are generalized and expanded by the results shown. An example and application to support our result is presented.</p></abstract>