The existence and uniqueness of fixed points for specific classes of contractive mappings in generalized metric spaces are examined in this paper. By easing the triangle inequality or substituting it with less stringent requirements, generalized metric spaces expand upon the traditional concept of metric spaces. Differential equations, computer science, optimization, and nonlinear analysis all benefit from such spaces. For Banach-type, Kannan-type, and Chatterjea-type contractions in generalized metric spaces, we prove novel fixed point theorems. The resulting results are validated by a number of illustrated instances. Additionally covered are iterative approximation techniques and applications to integral equations.

For Banach, Kannan, and Chatterjea type contractive mappings in generalized metric spaces, we proved a number of fixed point theorems. The presented results expand the applicability to areas where standard metrics fail and extend classical fixed point principles. The utility of these findings is demonstrated by examples and applications to integral equations and iterative techniques. Future work may focus on: multivalued mappings, fuzzy generalized metric spaces, probabilistic generalized spaces, coupled fixed points, applications in machine learning

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