Fixed Point Theorems of Random and Multivalued Mappings and Their Influence on Random Variational Problems

Minyan Zha

doi:10.47297/taposatWSP2633-456932.20260705

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Fixed Point Theorems of Random and Multivalued Mappings and Their Influence on Random Variational Problems

7卷第5期

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Fixed Point Theorems of Random and Multivalued Mappings and Their Influence on Random Variational Problems
Fixed Point Theorems of Random and Multivalued Mappings and Their Influence on Random Variational Problems
College of Mathematics and Statistics, Shaanxi Normal University, Xi'an, Shaanxi, 710001, China
2026年7卷第5期页码：165-170
网络首发：2026-07-15，

纸质出版：2026-05-30
DOI：10.47297/taposatWSP2633-456932.20260705
Accepted：

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Minyan Zha. (2026). Fixed Point Theorems of Random and Multivalued Mappings and Their Influence on Random Variational Problems. 科技理论与实践（英文版）, 7(5), 165-170.

Zha Minyan.Fixed Point Theorems of Random and Multivalued Mappings and Their Influence on Random Variational Problems[J].Theory and Practice of Science and Technology,2026,07(05):165-170.
Minyan Zha. (2026). Fixed Point Theorems of Random and Multivalued Mappings and Their Influence on Random Variational Problems. 科技理论与实践（英文版）, 7(5), 165-170. DOI： 10.47297/taposatWSP2633-456932.20260705.

Zha Minyan.Fixed Point Theorems of Random and Multivalued Mappings and Their Influence on Random Variational Problems[J].Theory and Practice of Science and Technology,2026,07(05):165-170. DOI： 10.47297/taposatWSP2633-456932.20260705.

摘要

Abstract

Fixed point theory serves as an essential means to analyze the inherent properties of nonlinear systems. As practical engineering and mathematical problems grow increasingly intricate

conventional theories based on deterministic single-valued mappings can hardly describe models featuring random interference and multiple solution branches. This paper conducts research on fixed point properties of stochastic multivalued mappings within the framework of complete metric spaces and probability measurable spaces. The research adopts Hausdorff metric

measurable selection principle and iterative convergence analysis as core research tools. Fundamental definitions and classical lemmas are sorted out at first. On this basis

this work establishes theorems concerning the existence and uniqueness of fixed points for stochastic multivalued contractive mappings

and further derives stability properties under parametric perturbation. With the help of convex projection transformation defined on Hilbert spaces

stochastic variational inequalities and variational inclusions are converted into equivalent fixed point solving problems. The proposed theorems are applied to judge whether solutions exist uniquely for such variational problems. Numerical examples are adopted to verify the validity of theoretical deductions

and the influence of varying stochastic parameters on system solutions is also discussed.

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references

S. Banach. Sur les Operations Dans les Ensembles Abstraits er leur Application aux Equations Integrals[J]. Fundamenta. Mathematicae, 1922, 3: 133-181.

W. R. Mann. Mean Value Method in Iteration[J]. Proceeding of the American Mathematical Society,1953, 4(3): 506-510.

B. Halpern. Fixed Points of Nonexpanding Maps[J]. Bulletin of the American Mathematical Society, 1967, 73(6): 957- 961.

H. K. Xu, R. G. Ori. An implicit iteration process for non-expansive mappings[J]. Numerical Functional Analysis and Optimization, 2001, 22(5): 767-773.

H. Zhang, X. L. Liu, J. Deng, Y. Sun. Strong converge-nce of modified inertial extragradient methods for non-Lipschitz continuous variational inequalities and fixed point problems[J]. Computational and Applied Mathematics, 2024, 43: 1-25.

G. M. Korpelevich. An Extragradient Method for Finding Saddle Points and for Other Problems[J]. Ekonomikai Matematicheskie Metody, 1976, 12(4): 747-756.

H. C. Zhang, Y. H. Qu, Y. F. Qu. The generalized viscosity implicit midpoint rule for non-expansive mappings in Banach Space[J]. Mathematics, 2019, 7(512): 1-16.

K. Wang, Y. H. Wang, S. Olaniyi, Y. Shehu. Double inertial projection method for variational inequalities with quasi-monotonicity[J]. A Journal of Mathematical Programming and Operations Research, 2024, 73(3): 707-739.

H. K. Xu, M. Alghamdi, N. Shahzad. The viscosity technique for the implicit midpoint rule of non-expansive mappings in Hilbert spaces[J]. Fixed Point Theory and Applications, 2015, 2015(41):1-12

Y. H. Yao, N. Shahzad, Y. C. Liou. Modified semi-implicit midpoint rule for non-expansive mappings[J]. Fixed Point Theory and Applications, 2015, 2015(166): 1-15.

S. Dhakal, W. Sintunavarat. The viscosity method for the implicit double midpoint rule with numerical resultsand its applications[J]. Computation and Applied Mathematics, 2019, 38(2): 1-18.

G. Cai, Q. L. Dong, Y. Peng. Inertial Viscosity Iterative Method for Solving Pseudo-monotone Variational Inequality Problems and Fixed Point Problems[J]. Acta Mathematica Sinica, English Series, 2022, 38(5): 937-952.