Study of Fixed-Point Existence and Uniqueness Results Based on the Sehgal-Guseman Contraction in Complete G-Metric Spaces

In recent years, there has been a significant rise in the application of b-metric spaces in mathematical and analytical studies, particularly regarding fixed-point theory. Nonetheless, these spaces present certain challenges. A key issue stems from their fundamental two-dimensional characteristics, which complicate the direct application or extension of results—especially fixed-point theorems—to higher-dimensional frameworks, such as three-dimensional spaces. Previous research has largely concentrated on fixed-point theorems within the realm of b-metric spaces, particularly those associated with the Sehgal-Guseman contraction principle. While these investigations have contributed valuable insights, they are limited in their breadth. To address this constraint, the current study introduces a new approach by presenting an alternative metric framework—specifically, the G-metric space. The main aim of this research is to generalize and expand the Sehgal-Guseman-type contraction results from the b-metric context to the more extensive and adaptable G-metric environment. This study explores the existence, uniqueness, and characteristics of fixed points under these generalized conditions using complete G-metric spaces.