New Generalization of Metric-Type Spaces—Strong Controlled

Abstract

In this manuscript, we establish a new type of metric space that is called controlled strong metric spaces by introducing a controlled function to the triangle inequality as follows: ℘(s,r)≤℘(s,z)+η(z,r)℘(z,r), and keeping the symmetry condition that is ℘(s,r)=℘(r,s)forallr,s. We demonstrate the existence of the fixed point of self-mapping and its uniqueness in such spaces that satisfy linear and nonlinear contractions. Moreover, we provide three applications of results to polynomial equations of high degree, systems of linear equations, along with fractional differential equations.

Keywords

• strong <i>b</i>−metric space (SbMS)
• a double-controlled metric type
• fixed-point and strong controlled metric-type space (SCMTS)