Convergence Result for Random Split Variational Inequality Problem Using a Two-Step Iterative Scheme in Hilbert Spaces.

Ekemini U. George; Akaninyene U. Udom; Matthew J. Iseh; Anthony E. Usoro

doi:10.52589/AJMSS-IR0ROAD2

Convergence Result for Random Split Variational Inequality Problem Using a Two-Step Iterative Scheme in Hilbert Spaces. | AB Journals

Convergence Result for Random Split Variational Inequality Problem Using a Two-Step Iterative Scheme in Hilbert Spaces.

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African Journal of Mathematics and Statistics Studies

Vol. 8Issue 42025pp. 109–125Published 2 December 2025

DOI 10.52589/AJMSS-IR0ROAD2

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Abstract:

The paper focuses on finding solution to stochastic split variational inequality problem, by extending the works done in classical functional analysis, to accommodate situations where there are perturbations in the system, as real life problems are, mostly, random in nature. Solution to the problem is sought through fixed point theory. A random two-step version of the hybrid steepest descent iterative scheme is used to obtain a fixed point solution to the problem. A numerical example is presented, to illustrate the workability of the result. A strong convergence result is also proven for the solution. This result extends, and generalizes some established results in literature on classical functional analysis.

Keywords:Stochastic split feasibility variational inequality monotone Hilbert spaces operator.

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