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We consider a general metric Steiner problem, which involves finding a set S with the minimal length, such that S ∪ A is connected, where A is a given compact subset of a given complete metric space X; a solution is called the Steiner tree. Paolini, Stepanov, and Teplitskaya in 2015 provided an example of a planar Steiner tree with an infinite number of branching points connecting an uncountable set of points. We prove that such a set can have a positive Hausdorff dimension, which was an open question (the corresponding tree exhibits self-similar fractal properties). [ABSTRACT FROM AUTHOR]

In this manuscript, some similar tripled fixed point results under certain restrictions on a b − metric space endowed with graphs are established. Furthermore, an example is provided to support our results. The obtained results extend, generalize, and unify several similar significant contributions in the literature. Finally, to further extend our results, the existence of a solution to a system of ordinary differential equations with infinite delay is derived. [ABSTRACT FROM AUTHOR]