APPROXIMATION RESULTS FOR SOLUTION OF STOCHASTIC HARD-SOFT CONSTRAINED CONVEX FEASIBILITY PROBLEM

AKANINYENE UDO UDOM *

Department of Statistics, University of Nigeria Nsukka, Enugu State, Nigeria.

CHIJIOKE JOEL NWEKE

Department of Mathematics and Statistics, Alex Ekwueme Federal University Ndufu-Alike, Ebonyi State, Nigeria.

GEORGE CHINANU MBAEYI

Department of Mathematics and Statistics, Alex Ekwueme Federal University Ndufu-Alike, Ebonyi State, Nigeria.

EVERESTUS O. OSSAI

Department of Statistics, University of Nigeria Nsukka, Enugu State, Nigeria.

*Author to whom correspondence should be addressed.


Abstract

In this work, a random-type iterative scheme is proposed and used for random approximation of the solution of stochastic convex feasibility problem involving hard constraints (that must be satisfied) and soft constraints (whose proximity function is minimized) in Hilbert space. The iterative algorithm is based on an alternating projection with lipschitzian and firmly non-expansive mapping. Convergence results of the random-type iterative scheme to the solution of the stochastic convex feasibility problem is proved. These will serve as an extension, unification and generalization of different established classic results in the literature.

Keywords: Hard and soft constraints, proximity function, random fixed-point, stochastic, firmly non-expansive


How to Cite

UDOM, A. U., NWEKE, C. J., MBAEYI, G. C., & OSSAI, E. O. (2022). APPROXIMATION RESULTS FOR SOLUTION OF STOCHASTIC HARD-SOFT CONSTRAINED CONVEX FEASIBILITY PROBLEM. Asian Journal of Mathematics and Computer Research, 29(3), 25–39. https://doi.org/10.56557/ajomcor/2022/v29i37957

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