A new iteration technique for nonlinear operators as concerns convex programming and feasibility problems

  • D. R. Sahu
  • A. PiteaEmail author
  • M. Verma
Original Paper


The aim of this work is to develop an S-iteration technique for finding common fixed points for nonself quasi-nonexpansive mappings in the framework of a uniformly convex Banach space. Convergence properties of the proposed algorithm are analyzed in the setting of uniformly convex Banach spaces. To prove the usability of our results, some novel applications are provided, focused on zeros of accretive operators, convex programming, and feasibility problems. Some numerical experiments with real datasets for Lasso problems are provided.


Accretive operator Convex programming Feasibility problem Fixed point S-iteration process 


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The second author has been funded by University Politehnica of Bucharest, through the “Excellence Research Grants” Program, UPB - GEX. Identifier: UPB-EXCELENŢĂ-2017, ID 53, no. int. SA 541702, “Analiză neliniară şi optimizări.”


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Authors and Affiliations

  1. 1.Department of MathematicsBanaras Hindu UniversityVaranasiIndia
  2. 2.Department of Mathematics and InformaticsUniversity Politehnica of BucharestBucharestRomania
  3. 3.Institute for Development and Research in Banking Technology (IDRBT)HyderabadIndia

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