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Ample Spectrum Contractions and Related Fixed Point Theorems

Author

Listed:
  • Antonio Francisco Roldán López de Hierro

    (Department of Statistics and Operations Research, University of Granada, 18010 Granada, Spain)

  • Naseer Shahzad

    (Department of Mathematics, Faculty of Science, King Abdulaziz University, P.O.B. 80203, Jeddah 21589, Saudi Arabia)

Abstract

Simulation functions were introduced by Khojasteh et al. as a method to extend several classes of fixed point theorems by a simple condition. After that, many researchers have amplified the knowledge of such kind of contractions in several ways. R -functions, ( R , S ) -contractions and ( A , S ) -contractions can be considered as approaches in this direction. A common characteristic of the previous kind of contractive maps is the fact that they are defined by a strict inequality. In this manuscript, we show the advantages of replacing such inequality with a weaker one, involving a family of more general auxiliary functions. As a consequence of our study, we show that not only the above-commented contractions are particular cases, but also another classes of contractive maps correspond to this new point of view.

Suggested Citation

  • Antonio Francisco Roldán López de Hierro & Naseer Shahzad, 2019. "Ample Spectrum Contractions and Related Fixed Point Theorems," Mathematics, MDPI, vol. 7(11), pages 1-23, November.
    • Handle: RePEc:gam:jmathe:v:7:y:2019:i:11:p:1033-:d:283043
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    References listed on IDEAS

    as
    1. Saleh A. Al-Mezel & Hamed H. Alsulami & Erdal Karapınar & Antonio-Francisco Roldán López-de-Hierro, 2014. "Discussion on “Multidimensional Coincidence Points” via Recent Publications," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-13, May.
    2. Wei-Shih Du & Farshid Khojasteh, 2014. "New Results and Generalizations for Approximate Fixed Point Property and Their Applications," Abstract and Applied Analysis, Hindawi, vol. 2014, pages 1-9, March.
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