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Strong Convergence Theorem for Finding a Common Solution of Convex Minimization and Fixed Point Problems in CAT(0) Spaces

Author

Listed:
  • P. V. Ndlovu
  • L. O. Jolaoso
  • Maggie Aphane

Abstract

In this paper, we introduce a proximal point algorithm for approximating a common solution of finite family of convex minimization problems and fixed point problems for k‐demicontractive mappings in complete CAT(0) spaces. We prove a strong convergence result and obtain other consequence results which generalize and extend some recent results in the literature. We further provide a numerical example to illustrate the convergence behaviour of the sequence generated by our algorithm.

Suggested Citation

  • P. V. Ndlovu & L. O. Jolaoso & Maggie Aphane, 2022. "Strong Convergence Theorem for Finding a Common Solution of Convex Minimization and Fixed Point Problems in CAT(0) Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2022(1).
    • Handle: RePEc:wly:jnlaaa:v:2022:y:2022:i:1:n:2960135
    DOI: 10.1155/2022/2960135
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    References listed on IDEAS

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    1. C. E. Chidume & A. U. Bello & P. Ndambomve, 2014. "Strong and Δ‐Convergence Theorems for Common Fixed Points of a Finite Family of Multivalued Demicontractive Mappings in CAT(0) Spaces," Abstract and Applied Analysis, John Wiley & Sons, vol. 2014(1).
    2. C. E. Chidume & A. U. Bello & P. Ndambomve, 2014. "Strong and -Convergence Theorems for Common Fixed Points of a Finite Family of Multivalued Demicontractive Mappings in CAT Spaces," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-6, October.
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