Wangwe, Lucas2026-04-222026-04-222025https://repository.must.ac.tz/handle/123456789/571Mbeya university of science and technologyThis article explores the fixed point theorem for a novel class of interpolative relation theoretical convex mappings in TVS-valued cone metric spaces, integrating relational theory, convexity, and interpolation properties to offer fresh perspectives and possible uses in theoretical and applied mathematics. An application of the results to differential equations and matrix equations in the context of orthogonal TVS-valued cone metric spaces is presented, along with a constructive example to support the findings.enArticle