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Approximating fixed points for nonlinear generalized mappings using Ishikawa iteration

Abstract

We obtain a contractive condition for the existence and uniqueness of fixed points for a generalized contraction-type mapping. The present study focuses on providing a method for the existence of fixed points for nonlinear mappings. Sufficient conditions for the existence and uniqueness of such points are obtained using Ishikawa iteration process. Moreover, an example is given.

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Acknowledgements

The author is thankful to his Phd coordinator, professor dr. Adrian Petruşel from Babeş - Bolyai University, for his support and useful suggestions throughout the entire article.

Funding

This research did not receive any specific grant from funding agencies in the public, commercial, or not-for-profit sectors.

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Correspondence to Cristian Daniel Alecsa.

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Alecsa, C.D. Approximating fixed points for nonlinear generalized mappings using Ishikawa iteration. Rend. Circ. Mat. Palermo, II. Ser 68, 163–191 (2019). https://doi.org/10.1007/s12215-018-0349-7

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  • DOI: https://doi.org/10.1007/s12215-018-0349-7

Keywords

  • Fixed point
  • Generalized contraction
  • Ishikawa
  • Convergence
  • Convex metric space

Mathematics Subject Classification

  • 47H10
  • 54H25