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Oluwatosin Temitope Mewomo, Abd-semii Oluwatosin-Enitan Owolabi, Timilehin Opeyemi Alakoya, Lanre Akinyemi, On split null point and fixed point problems for demimetric mappings

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DOI: 10.23952/asvao.8.2026.3.04
Volume 8, Issue 3, 1 December 2026, Pages 337-355

 

Abstract. The Split Null Point Problem (SNPP) was extensively studied due to its wide applications and various iteration methods were proposed for its solution. However, most of the existing methods in the literature require prior knowledge of the operator norm, which in most cases is very difficult or almost impossible to compute or even estimate. In this paper, we study the SNPP of maximal monotone mappings and fixed point problems of demimetric mappings. We introduce a self-adaptive step size algorithm of inertial viscosity method for finding a common solution of the problems. The self-adaptive step size ensures no requirement for a prior knowledge or estimate of the norm of the operator. Under mild conditions, we obtain strong convergence of the proposed algorithm. Finally, we present some applications and numerical examples to demonstrate the performance of our method and compare with some related methods. Our results extend and improve several related results in the literature.

 

How to Cite this Article:
O.T. Mewomo, A.S.O.E. Owolabi, T.O. Alakoya, L. Akinyemi, On split null point and fixed point problems for demimetric mappings, Appl. Set-Valued Anal. Optim. 8 (2026), 337-355.