Existence results for trifunction equilibrium problems and fixed point problems

  • Nihar Kumar Mahato
  • Muhammad Aslam Noor
  • Nabin Kumar Sahu


In this paper, we establish the existence and uniqueness solutions of trifunction equilibrium problems using the generalized relaxed \(\alpha \)-monotonicity in Banach spaces. By using the generalized f-projection operator, a hybrid iteration scheme is presented to find a common element of the solutions of a system of trifunction equilibrium problems and the set of fixed points of an infinite family of quasi-\(\phi \)-nonexpansive mappings. Moreover, the strong convergence of our new proposed iterative method under generalized relaxed \(\alpha \)-monotonicity is considered.


Quasi-\(\phi \)-nonexpansive mapping Normalized duality mapping General metric projection General f-projection operator Generalized relaxed \(\alpha \)-monotonicity 

Mathematics Subject Classification

47J05 47H09 49J25 


Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interests.


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Copyright information

© Springer International Publishing AG 2017

Authors and Affiliations

  • Nihar Kumar Mahato
    • 1
  • Muhammad Aslam Noor
    • 2
  • Nabin Kumar Sahu
    • 3
  1. 1.Natural Science (Mathematics), Indian Institute of Information TechnologyDesign and ManufacturingJabalpurIndia
  2. 2.Mathematics DepartmentCOMSATS Institute of Information TechnologyIslamabadPakistan
  3. 3.Dhirubhai Ambani Institute of Information and Communication TechnologyGandhinagarIndia

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