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Dynamic stepsize iteration process for solving split common fixed point problems with applications

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  • Kumar, Ajay
  • Thakur, Balwant Singh
  • Postolache, Mihai

Abstract

In this paper, we study the split common fixed point problem for two nonlinear mappings in p-uniformly convex and uniformly smooth Banach spaces. We propose an algorithm which uses dynamic stepsize, it allows to be easily implemented without prior information about operator norm. We further apply our result to solve the split variational inclusion problem, equilibrium problem and convexly constrained linear inverse problem. Moreover, we provide numerical examples to verify efficiency of our algorithm.

Suggested Citation

  • Kumar, Ajay & Thakur, Balwant Singh & Postolache, Mihai, 2024. "Dynamic stepsize iteration process for solving split common fixed point problems with applications," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 218(C), pages 498-511.
    • Handle: RePEc:eee:matcom:v:218:y:2024:i:c:p:498-511
    DOI: 10.1016/j.matcom.2023.12.005
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    References listed on IDEAS

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    1. A. Moudafi, 2011. "Split Monotone Variational Inclusions," Journal of Optimization Theory and Applications, Springer, vol. 150(2), pages 275-283, August.
    2. Simeon Reich & Shoham Sabach, 2011. "Existence and Approximation of Fixed Points of Bregman Firmly Nonexpansive Mappings in Reflexive Banach Spaces," Springer Optimization and Its Applications, in: Heinz H. Bauschke & Regina S. Burachik & Patrick L. Combettes & Veit Elser & D. Russell Luke & Henry (ed.), Fixed-Point Algorithms for Inverse Problems in Science and Engineering, chapter 0, pages 301-316, Springer.
    3. Li-Wei Kuo & D. R. Sahu, 2013. "Bregman Distance and Strong Convergence of Proximal-Type Algorithms," Abstract and Applied Analysis, Hindawi, vol. 2013, pages 1-12, July.
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