In this paper, we introduce the notion of a rectangular S-b-metric space which extends the rectangular metric space given by Branciari [3]. We establish some fixed point theorems in this new structure. We provide some applications of our results in differential and integral equations.
In this paper, we consider the Korteweg-de Vries equation with internal time-varying delay feedback. We prove exponential stability results using an appropriate Lyapunov functional, without imposing any assumptions on the length of the spatial domain. Finally, we present numerical simulations to illustrate the stability results obtained.
Two fixed point theorems for alpha-admissible mappings satisfying contractive conditions of integral type with w-distance in a complete metric space are demonstrated. The results obtained in this paper improve and generalize some well-known results in the literature. An example is given.
In the present work, using the Matkowski type contraction, we discuss the existence of fixed point results within the framework of orthogonal c-metric spaces. Our results extend and generalize several well-known findings that are already present in the literature. Furthermore, as an application, we investigate solution to a nonlinear integral equation.
This paper investigates fixed point theorems in bipolar R-metric space by introducing the concepts of F-R-contractive and F-R-expansive maps. We first establish a fixed point theorem for F-R-contractive map, then extend our results to F-R-expansive map. Our findings reveal that under certain conditions, these results can be reduced to novel fixed point results for expansive maps in bipolar metric space. This aligns with existing literature, underscoring the relevance, and applicability of our findings in broader contexts.
