FIXED POINT THEOREMS FOR SEQUENCE OF MAPPINGS IN TRICOMPLEX VALUED METRIC SPACE

Fixed point theory plays a crucial role in mathematical analysis, with profound applications in differential equations, optimization, and dynamic systems. Over the years, researchers have extended classical fixed point results to more complex structures, such as tricomplex valued metric spaces, to address problems in multidimensional and hypercomplex settings. Despite the growing interest in tricomplex variable spaces, existing literature on fixed point theorems within these frameworks remains limited by various constraints. The existing literature exhibits several limitations; therefore, in this article, we utilize the concepts of continuity and weak compatibility to establish fixed point results for a novel class of contraction mappings by employing a sequence of mappings within a tricomplex valued metric space. If two mappings commute at their point of coincidence, they are said to be weakly compatible. These results not only deepen the comprehension of fixed point theory but also open up new possibilities for its application in more intricate and varied mathematical contexts. As a result, our research progresses in the field, providing a solid foundation for future investigations and potential uses across multiple scientific and engineering domains.