Approximation of a common f-fixed point of f-pseudocontractive mappings in Banach spaces

Abstract

Let E be a real reflexive Banach space with its dual \(E^*\) and f be a proper, convex and lower-semi-continuous function on E. The purpose of this paper is to introduce and study a new class of mappings from E into \(E^*\) called f-pseudocontractive mappings with the notion of f-fixed points. In the case that E is a real  reflexive Banach space and f is a strongly coercive, bounded and uniformly Fréchet differentiable Legendre function which is strongly convex on bounded subsets of E, a sequence is constructed which converges strongly to a common f-fixed point of two f-pseudocontractive mappings. As a consequence, we obtain a scheme which converges strongly to a common zero of monotone mappings. Furthermore, this analog is applied to approximate solutions to convex optimization problems. Our results improve and generalize many of the results in the literature.

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Acknowledgements

The authors express their deep gratitude to the referees and the editor for their valuable comments and suggestions

Funding

Both authors are gratefully acknowledge the funding received from Simons Foundation based at Botswana International University of Science and Technology (BIUST).

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Correspondence to Habtu Zegeye.

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Zegeye, H., Wega, G.B. Approximation of a common f-fixed point of f-pseudocontractive mappings in Banach spaces. Rend. Circ. Mat. Palermo, II. Ser (2020). https://doi.org/10.1007/s12215-020-00549-8

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Keywords

  • Banach spaces
  • f-Fixed point
  • f-Pseudocontractive mapping
  • Monotone mapping
  • Semi-fixed points
  • Semi-pseudocontractive mapping
  • Strong convergence
  • Zero points

Mathematics Subject Classification

  • 46N10
  • 47H05
  • 47H06
  • 47h09
  • 47H10
  • 47J25
  • 90C25