Common solution to an equilibrium problem and a fixed point problem for an asymptotically quasi-\(\phi \)-nonexpansive mapping in intermediate sense

Abstract

In this paper, we introduce and study an iterative method for solving an equilibrium problem and a fixed point problem for an asymptotically quasi-\(\phi \)-nonexpansive mapping in intermediate sense in Banach space. We prove that the sequences generated by iterative algorithm converge strongly to a common solution of these problems in a uniformly smooth and strictly convex Banach space.

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Acknowledgments

The authors are very grateful to the anonymous referee for his valuable comments toward the improvement of the paper. The second author is thankful to the University Grant Commission, Government of India, New Delhi for BSR (Basic Scientific Research) fellowship to support this research work.

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Correspondence to K. R. Kazmi.

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Kazmi, K.R., Ali, R. Common solution to an equilibrium problem and a fixed point problem for an asymptotically quasi-\(\phi \)-nonexpansive mapping in intermediate sense. RACSAM 111, 877–889 (2017). https://doi.org/10.1007/s13398-016-0331-1

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Keywords

  • Equilibrium problem
  • Asymptotically quasi-\(\phi \)-nonexpansive mapping in intermediate sense
  • Hybrid iterative method

Mathematics Subject Classification

  • 47H05
  • 47H09
  • 47J25