ATTRACTIVE POINT APPROXIMATIONS OF FURTHER 2-GENERALIZED HYBRID MAPPING IN HYPERBOLIC SPACE
ABSTRACT
In this research study, we introduce a novel iterative scheme based on viscosity principles. We demonstrate that this scheme exhibits strong convergence towards the attractive point of a 2-generalized hybrid mapping in hyperbolic spaces. Our findings significantly enhance existing results in the literature, contributing to the advancement of this field.
In this research work, the focus is on proposing and analyzing a viscosity type iterative scheme. This scheme is designed to converge strongly towards the attractive point of a 2-generalized hybrid mapping in hyperbolic spaces.
Viscosity methods are commonly employed in iterative algorithms to handle problems with non-smooth or nonconvex functions. These methods incorporate a measure of the local behavior of the function, known as the viscosity solution, which guides the iterative process towards the desired solution.
Hyperbolic spaces, on the other hand, are a type of non-Euclidean geometry where the parallel postulate of Euclidean geometry does not hold. These spaces have unique geometric properties and find applications in various fields, such as physics, computer science, and mathematics.
By applying the proposed viscosity type iterative scheme to the 2-generalized hybrid mapping in hyperbolic spaces, the research demonstrates its strong convergence. Strong convergence implies that the iterative process reliably reaches the desired attractive point of the mapping, providing a robust and effective solution.
Furthermore, the research highlights that the presented scheme improves upon existing results in the literature. This suggests that the proposed approach offers advancements in terms of convergence behavior, efficiency, or applicability compared to previous methods studied in the field.
Overall, this research contributes to the understanding and development of iterative algorithms in hyperbolic spaces, offering new insights and potentially opening up avenues for further investigations and applications in related domains.
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