On synchronal algorithm for fixed point and variational inequality problems in hilbert spaces

Area of Science:

• Mathematical Analysis
• Functional Analysis
• Numerical Analysis

Background:

• Fixed point theory and variational inequality problems are crucial in applied mathematics.
• Approximation methods provide tools for solving these problems numerically.
• Generalizing existing methods enhances their applicability and robustness.

Purpose of the Study:

• To extend and generalize approximation methods for [Formula: see text]-total asymptotically strict pseudocontractions.
• To apply these generalized methods to solve fixed point problems.
• To apply these generalized methods to solve variational inequality problems within Hilbert spaces.

Main Methods:

• Utilizing approximation techniques within Hilbert space framework.
• Developing and analyzing iterative algorithms for pseudocontraction mappings.
• Establishing convergence criteria for the proposed methods.

Main Results:

• The paper successfully generalizes approximation methods for a specific class of mappings.
• Demonstrated the effectiveness of the proposed methods in solving fixed point problems.
• Showcased the applicability of the methods to variational inequality problems.

Conclusions:

• The generalized methods offer improved performance and broader applicability.
• The findings extend and enhance existing literature on approximation methods.
• This work contributes to the theoretical and practical understanding of solving complex mathematical problems.