Coupled Fixed Point Theorems in G-metric Spaces via Α-series

Document Type : Research Paper

Authors

1 Department of Mathematics, Ardabil Branch, Islamic Azad University, Ardabil, Iran

2 Department of Mathematics, Ardabil Branch Islamic Azad University, Ardabil, Iran

Abstract

The object of this paper is to study of the results of coupled fixed point in generalized metric spaces, as known as G-metric spaces. We will impose some conditions upon a self-mapping and a sequence of mappings via a kind of series, known as a-series. Also, an example is provided to illustrate the results.

Keywords


  1. H. Aydi, B. Damjanovic, B. Samet, W. Shatanawi, Coupled fixed point theorems for nonlinear contractions in partially ordered G-metric spaces, Math. Comput. Modell., 54, 2443-2450 (2011).
  2. T.G. Bhaskar, V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65, 1379-1393 (2006).
  3. B. S. Choudhary, A. Kundu, A coupled coincidence point result in partially ordered metric spaces for compatible mappings, Nonlinear Anal., 73, 2524-2531 (2010).
  4. S. Hadi Bonab, R. Abazari, A. Bagheri Vakilabad, Partially ordered cone metric spaces and coupled fixed point theorems via α-series, MACA, 1 (1), 50-61 (2019).
  5. S. Hadi Bonab, R. Abazari, A. Bagheri Vakilabad, H. Hosseinzadeh, Generalized metric spaces endowed with vector-valued metrics and matrix equations by tripled fixed point theorems, J. Inequal. Appl., 2020, 1-16 (2020).
  6. H. Hosseinzadeh, Some Fixed Point Theorems in Generalized Metric Spaces Endowed with Vector-valued Metrics and Application in Linear and Nonlinear Matrix Equations, Sahand Commun. Math. Anal., 17, 37-53 (2020).
  7. V. Lakshmikantham, L. Ciric, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Anal., 70, 4341-4349 (2009).
  8. Z. Mostafa, A new structure for generalized metric spaces with applications to fixed point theory, Ph.D. thesis, The University of Newcastle, Callaghan, Australia, (2005).
  9. Z. Mostafa, B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex Anal., 7 (2), 289-297 (2006).
  10. RK. Vats, K. Tas, V. Sihag and A. Kumar, Triple fixed point theorems via α-series in partially ordered metric spaces, J. Inequal. Appl., 1-12 (2014).
  11. V. Sihag, C. Vetro, RK. Vats, A fixed point theorem in G-metric spaces via α-series, Quaest. Math., 37, 1-6 (2014).
  12. S.H. Rasouli, M.H. Malekshah, Coupled fixed point results for mappings without mixed monotone property in partially ordered G-metric spaces, J. Egyptian Math. Soc., 22, 471–475 (2014).