A Fixed Point Technique for Solving Boundary Value Problems in Branciari Suprametric Spaces

Branciari Suprametric Spaces

Abstract

The focus of the present article is to initiate the notion of Branciari suprametric spaces and to investigate some of its fundamental topological properties. An illustration is provided to validate the newly defined idea of Branciari suprametric spaces. Further two intriguing, fixed point results are proved, and a corollary is presented as an implication of our main result. The following is a specification of the analogue of the rectangle inequality in Branciari suprametric spaces $d_\mathcal{B}(\tau,\iota) \leq d_\mathcal{B}(\tau,\nu) + d_\mathcal{B}(\nu,\sigma) + d_\mathcal{B}(\sigma,\iota) + \mu d_\mathcal{B}(\tau,\nu) d_\mathcal{B}(\nu,\sigma) d_\mathcal{B}(\sigma,\iota)$ for all $\tau\neq \nu, \nu\neq \sigma$ and $\sigma\neq \iota$. Furthermore, by employing the results obtained, the present study intends to provide an appropriate solution for the nonlinear fractional differential equations of the Riemann-Liouville type.