In this paper, we examine fixed point theory in the context of complete b-metric spaces, specifically for a class of generalized Reich-type rational contractions. Fixed point theory is a prominent branch of mathematical analysis, with numerous applications in functional analysis, differential and integral equations, optimization problems, and applied mathematics. A b-metric space is a generalization of a standard metric space, achieved through the modification of the classical triangle inequality by a coefficient, facilitating the examination of a broader class of spaces for which convergence and fixed point theorems can be proven. This flexibility in analysis is especially useful when dealing with complex mathematical models and real-world applications, where strict metric properties may not be applicable.

We prove the existence and uniqueness of fixed points for mappings that satisfy a rational Reich-type contractive condition, which generalizes classical contraction principles by taking into account a rational function of distances between points and their images. Our method of proof involves the construction of an iterative sequence in the b-metric space and proving that it is a Cauchy sequence. By making use of the relaxed triangle inequality that corresponds to the b-metric constant, we show that this sequence converges to a unique fixed point, thus proving both existence and uniqueness.

Moreover, our results generalize several classical fixed point theorems. Specifically, Banach-type, Kannan-type, and classical Reich-type contraction mappings can be obtained by selecting appropriate parameters in the rational contractive condition. This shows the generality of our method of proof, which combines several strands of fixed point theory and generalizes them to generalized b-metric spaces. The work lays a basis for further research in the field of nonlinear analysis.