10.30495/maca.2022.1949822.1046

A novel coupled fixed point results pertinent to Ab-metric spaces with application to integral equations

  1. Department of Mathematics, G.M.R. Institute of Technology, Rajam, Srikakulam-532127, India
  2. Department of Mathematics, Andhra University, Visakhapatnam-530001, India
  3. Department of Mathematics, Government Degree College, Palakonda, Srikakulam-532440, India

Published in Issue 2022-04-01

How to Cite

A novel coupled fixed point results pertinent to Ab-metric spaces with application to integral equations. (2022). Mathematical Analysis and Its Contemporary Applications, 4(3). https://doi.org/10.30495/maca.2022.1949822.1046

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Abstract

We prove the existence and uniqueness of coupled common fixed point results in partially ordered Ab-metric spaces in the present study. In addition to the acquired results, examples and applications are provided.

Keywords

  • Mixed weakly monotone property,
  • A-metric space,
  • Ab-metric with index n,
  • Ab-metric space,
  • Integral equation

References

  1. A. Aghajani, M. Abbas and E. Pourhadi Kallehbasti, Coupled fixed point theorems in partially ordered metric spaces and application, Math. Commun., 17(2012), 497-509.
  2. M.Abbas,B.Ali and Y.I.Suleiman, Generalized coupled common fixed point results in partially ordered A-metric spaces, Fixed Point Theory Appl., 2015(2015), 24 pages.
  3. T. Abeljawad, K. Abodayeh and N. M. Mlaiki, On fixed point generalizations to partial b-metric spaces, J. Comput. Anal. Appl., 19(2015), 883-891.
  4. I. A. Bakhtin, The contraction mapping principle in almost metric space, (Russian) Functional analysis, Ulyanovsk.Gos. Ped. Inst., Ulyanovsk, (1989), 26-37.
  5. J. Banas and D. O'Regan, On existence and local attractivity of solutions of a quadratic Volterra integral equation of fractional order, J. Math. Anal. Appl., 345(2008), 573-582.
  6. T. Gnana Bhaskar and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Anal., 65(2006), 1379-1393.
  7. M. E. Gordji, E. Akbar Tatar, Y. J. Cho and M. Ramezani, Coupled common fixed point theorems for mixed weakly monotone mappings in partially ordered metric spaces, Fixed Point Theory Appl., 95(2012), 12 pages.
  8. N. Hussain and Z.D. Mitrovic, On multi valued weak quasi-contractions in b-metric spaces, J. Nonlinear. Sci. Appl., 10(2017), 3815-3823.
  9. J. G. Mehta and M. L. Joshi, On coupled fixed point theorem in partially ordered complete metric spaces, Int. J. Pure Appl. Sci. Technol., 1 (2010), 87-92.
  10. N. Mlaiki and Y.Rohen, Some coupled fixed point theorem in partially ordered Ab-metric spaces, J. Nonlinear. Sci. Appl., 10(2017), 1731-1743.
  11. K. Ravibabu, Ch. Srinivasarao and Ch. Ragavendra Naidu, Coupled Fixed point and coinci-dence point theorems for generalized contractions in metric spaces with a partial order, Ital. J. Pure Appl. Math., 39(2018), 434-450.
  12. M. Ughade, D. Turkoglu, S. R. Singh and R. D. Daheriya, Some fixed point theorems in Ab-metric space, Br. J. Math. Comput. Sci., 19(2016), 1-24.