In this paper, we obtain the existence and uniqueness of the solution for three self mappings in a complete bipolar metric space under a new Caristi type contraction with an example. We also provide applications to homotopy theory and nonlinear integral equations.

In this paper, we introduce the concept of multivalued contraction mappings in partially ordered bipolar metric spaces and establish the existence of unique coupled fixed point results for multivalued contractive mapping by using mixed monotone property in partially ordered bipolar metric spaces. Some interesting consequences of our results are obtained.

In this paper, we establish the existence and uniqueness of common coupled fixed point results for three covariant mappings in bipolar metric spaces. Moreover, we give an illustration which presents the applicability of the achieved results also we provided applications to homotopy theory as well as integral equations.

In this paper, using rational type contractions, common fuzzy fixed point result for Φ contractive mappings involving control functions as coefficients of contractions in the setting of complex‐valued metric space is established. The derived results generalizes some result in the existing literature. To show the validity of the derived results an appropriate example and applications are also discussed.

This paper introduces a novel semicircular distribution obtained by applying the quadratic rank transmutation map to the stereographic semicircular exponential distribution, referred to as the transmuted stereographic semicircular exponential distribution (TSSCED). This newly proposed distribution exhibits enhanced flexibility compared to the baseline stereographic semicircular exponential distribution (SSCEXP). We conduct a comprehensive analysis of the model’s properties and demonstrate its efficacy in data modeling through the application to a real dataset.

In this paper we give some applications to integral equations as well as homotopy theory via fixed point theorems in partially ordered complete $S_{b}$S b -metric spaces by using generalized contractive conditions. We also furnish an example which supports our main result.