Viscosity approximation method for modified split generalized equilibrium and fixed point problems

• Hammed Anuoluwapo Abass ^[1] ; Chinedu Izuchukwu ^[1] ; Oluwatosin Temitope Mewomo ^[1]
  1. [1] University of KwaZulu-Natal

     University of KwaZulu-Natal

     Ethekwini, Sudáfrica

     
• Localización: Revista de la Unión Matemática Argentina, ISSN 0041-6932, ISSN-e 1669-9637, Vol. 61, Nº. 2, 2020, págs. 389-411
• Idioma: inglés
• DOI: 10.33044/revuma.v61n2a13
• Enlaces
  • Texto completo
• Resumen

  • We introduce a viscosity iterative algorithm for approximating a common solution of a modified split generalized equilibrium problem and a fixed point problem for a quasi-pseudocontractive mapping which also solves some variational inequality problems in real Hilbert spaces. The proposed iterative algorithm is constructed in such a way that it does not require the prior knowledge of the operator norm. Furthermore, we prove a strong convergence theorem for approximating the common solution of the aforementioned problems. Finally, we give a numerical example of our main theorem. Our result complements and extends some related works in the literature.