An Extended Almost Weak Contraction in Relational Metric Space and Applications to Nonlinear Matrix Equations

This manuscript investigates certain fixed point outcomes for an extended almost weak contraction map in a metric space equipped with a locally transitive binary relation. The insights achieved here improve, broaden, solidify and advance a number of noteworthy findings. We formulate a metrical fixed point theorem for almost Boyd–Wong contractions in the course of the procedure. We provide numerous examples of illustration in favour of our findings. Our results enable us to find a unique solution to a class of nonlinear matrix equations.