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Viscosity Iterative algorithm for solving Variational Inclusion and Fixed point problems involving Multivalued Quasi-Nonexpansive and Demicontractive Operators in real Hilbert Space

Furmose Mendy, John T Mendy

Abstract

This paper presents a modified general viscosity iterative process designed to solve variational inclusion and fixed point problems involving multi-valued quasi-nonexpansive and demi-contractive operators. The modified iterative process incorporates a viscosity approximation technique to handle the nonexpansive and contractive mappings, providing a more robust and efficient solution approach. By introducing an additional sequence of iterates, the algorithm iteratively approximates the desired solution by combining fixed point iteration with viscosity approximation. The proposed method has been proven to converge strongly to the solution of the given problem, ensuring the reliability and accuracy of the results.

Viscosity Iterative algorithm for solving Variational Inclusion and Fixed point problems involving Multivalued Quasi-Nonexpansive and Demicontractive Operators in real Hilbert Space

Abstract

This paper presents a modified general viscosity iterative process designed to solve variational inclusion and fixed point problems involving multi-valued quasi-nonexpansive and demi-contractive operators. The modified iterative process incorporates a viscosity approximation technique to handle the nonexpansive and contractive mappings, providing a more robust and efficient solution approach. By introducing an additional sequence of iterates, the algorithm iteratively approximates the desired solution by combining fixed point iteration with viscosity approximation. The proposed method has been proven to converge strongly to the solution of the given problem, ensuring the reliability and accuracy of the results.
Paper Structure (4 sections, 10 theorems, 59 equations)

This paper contains 4 sections, 10 theorems, 59 equations.

Table of Contents

  1. Introduction
  2. Mathematical Preliminaries
  3. Main Results
  4. Conclusion

Key Result

Theorem 1

Let $H$ be a real Hilbert space and $\mathbb{K}$ be a nonempty, closed convex subset of $H$. Let $\Lambda : \mathbb{K} \to H$ be an $\alpha-$inverse strongly monotone operator and let $\Phi : H \to H$ be an $k-$strongly monotone and $L-$Lipschitzian operator. Let $\varphi : \mathbb{K} \to H$ be an $ where $\{\beta_{n}\}, \{\gamma_{n}\}, \{\theta_{n}\} , \{\lambda_{n}\}$ and $\{\alpha_{n}\}$ are

Theorems & Definitions (15)

  • Definition 1
  • Example 1
  • Example 2
  • Example 3
  • Theorem 1
  • Theorem 2
  • Lemma 1
  • Lemma 2
  • Lemma 3
  • Lemma 4
  • ...and 5 more