Asia Mathematika, Vol 9, issue 2, pages: 1--11.

Fixed Point Results for General Integral Type Contraction Mappings in Cone Metric Spaces with Banach Algebra

Anil Kumar Mishra
Department of Mathematics, Government V.Y.T. Autonomous P.G. College, Durg, Chhattisgarh, India.
Padmavati
Department of Mathematics, Government V.Y.T. Autonomous P.G. College, Durg, Chhattisgarh, India.

Received: 10 May 2025 | Accepted: 18 Jul 2025 | Final Version: 31 Aug 2025

Abstract

The aim of this paper is to present a novel concept of generalized integral type contraction mapping in relation to a cone. The approach developed by F. Khojasteh is ultimately expanded under specific new contractive conditions of integral mapping to demonstrate fixed point results within the framework of cone metric spaces.

Keywords:
Banach algebra, generalized integral type contraction mapping, cone metric space.

1. Introduction

Huang and Zhang [1] introduced the cone metric space (CMS) in 2007...

References

  1. D. Ali Abdulsada, L. A. A. Al-Swidi, M. H. Hadi, On NCT-set theory, Neutrosophic Sets and Systems, vol. 68 (2024).
  2. K. Atanassov, Intuitionistic fuzzy sets, Fuzzy Sets and Systems 20 (1986), 87–96.
  3. G. B. Chae, J. Kim, J. G. Lee, K. Hur, Interval-valued intuitionistic sets and their application to topology, Annals of Fuzzy Mathematics and Informatics, vol. 21, no. 1 (Feb. 2021), pp. 1–28.
  4. D. Çoker, A note on intuitionistic sets and intuitionistic points, Turkish Journal of Mathematics, 20 (1996), 343–351.
  5. D. Çoker, An introduction to intuitionistic topological spaces, BUSEFAL 81 (2000), 51–56.
  6. S. Durga, L. Vidyarani, M. Vignheshwaran, T. Witczak, An introduction to picture topological spaces, Asia Mathematika, vol. 7, issue 3 (2023).
  7. S. Durga, L. Vidyarani, M. Vignheshwaran, T. Witczak, Properties of frontier, exterior and border in picture topological spaces, Turkish Journal of Mathematics, vol. 49, no. 1 (2025).
  8. J. H. Kim, P. K. Lim, J. G. Lee, K. Hur, Intuitionistic topological spaces, Annals of Fuzzy Mathematics and Informatics, vol. 15(2), pp. 101–122, 2018.
  9. A. G. Raoof, T. H. Jassim, Double intuitionistic continuous function in double intuitionistic topological spaces, Tikrit Journal of Pure Science, vol. 27(5) (2022).
  10. A. A. Salama, S. A. Alblowi, Neutrosophic set and neutrosophic topological spaces, IOSR Journal of Mathematics, vol. 3, pp. 31–35, 2012.
  11. A. M. Seif, Multi-fuzzifying topology, Asia Mathematika, vol. 8, issue 3 (2024), pp. 42–58.
  12. S. Ganesan, F. Smarandache, Some new classes of neutrosophic minimal open sets, Asia Mathematika, vol. 5, issue 1 (2021), pp. 103–112.
  13. F. Smarandache, Neutrosophy and neutrosophic logic, First International Conference on Neutrosophy, Neutrosophic Logic Set, Probability and Statistics, University of New Mexico, Gallup, NM, USA, 2002.
  14. O. A. E. Tantawy, S. A. El-Sheikh, S. Hussien, Topology of soft double sets, Annals of Fuzzy Mathematics and Informatics, vol. 12, no. 5 (Nov. 2016), pp. 641–657.
  15. Yong-jin L., Weak rough sets, Online PDF.
  16. T. Witczak, A note on the algebra of triple sets, Asia Mathematika, vol. 7, issue 2 (2023), pp. 15–33.
  17. T. Witczak, On the algebra of possibly paraconsistent sets, Neutrosophic Sets and Systems, vol. 73 (2024).
  18. L. Zadeh, Fuzzy sets, Information and Control, vol. 8(3), pp. 338–353, 1965.