A Fixed Point Result for Orthogonal Quasi- Contraction Mappings in O-Complete Super metric Spaces

Fixed point theory, rooted in the Banach Fixed Point Theorem, has been extended through concepts like quasi-contractions, orthogonal sets, and super metric spaces to handle broader classes of mappings. These generalizations enable applications in complex settings such as nonlinear operators and fractional differential equations, where classical metric frameworks are insufficient. This article introduces a fixed-point theorem for Orthogonal Quasi-Contraction mapping within the framework of o-complete super metric space. The result is supported by illustrative examples. In conclusion, the study advances fixed-point theory by extending it to more generalized spaces, enabling broader applications in complex non-linear systems. This work not only extends existing fixed-point theory but also opens avenues for further research in the study of non-linear mappings in more abstract space.