A viscosity-based iterative method for solving split generalized equilibrium and fixed point problems of strict pseudo-contractions

Saud Fahad Aldosary; Mohammad Farid; Saud Fahad Aldosary; Mohammad Farid

doi:10.3934/math.2025401

AIMS Mathematics

2025, Volume 10, Issue 4: 8753-8776. doi: 10.3934/math.2025401

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A viscosity-based iterative method for solving split generalized equilibrium and fixed point problems of strict pseudo-contractions

Saud Fahad Aldosary ¹,
Mohammad Farid ^{2
,
,}

1.
Department of Mathematics, College of Science and Humanities in Alkharj, Prince Sattam bin Abdulaziz University, Alkharj 11942, Saudi Arabia
2.
Department of Mathematics, College of Science, Qassim University, Saudi Arabia

Received: 31 January 2025 Revised: 27 March 2025 Accepted: 03 April 2025 Published: 16 April 2025
MSC : 47H05, 47H09, 47J20, 47J25

In this paper, we developed a viscosity-based extragradient iterative algorithm to approximate the solution of the split generalized equilibrium problem, the variational inequality problem, and the fixed point problem for a finite family of $ \epsilon $-strict pseudo-contractive and a nonexpansive mapping in Hilbert space. The main purpose was to establish strong convergence of the proposed algorithm under suitable conditions. We presented a comprehensive computational analysis to illustrate the effectiveness of our method and compared its performance with existing approaches. Our results extend and unify several well-known results in the literature, contributing significantly to the field.
Citation: Saud Fahad Aldosary, Mohammad Farid. A viscosity-based iterative method for solving split generalized equilibrium and fixed point problems of strict pseudo-contractions[J]. AIMS Mathematics, 2025, 10(4): 8753-8776. doi: 10.3934/math.2025401

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Abstract

In this paper, we developed a viscosity-based extragradient iterative algorithm to approximate the solution of the split generalized equilibrium problem, the variational inequality problem, and the fixed point problem for a finite family of $ \epsilon $-strict pseudo-contractive and a nonexpansive mapping in Hilbert space. The main purpose was to establish strong convergence of the proposed algorithm under suitable conditions. We presented a comprehensive computational analysis to illustrate the effectiveness of our method and compared its performance with existing approaches. Our results extend and unify several well-known results in the literature, contributing significantly to the field.

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