DOI QR코드

DOI QR Code

ON A COMMON FIXED POINT THEOREM IN INTUITIONISTIC MENGER SPACE VIA C CLASS AND INVERSE C CLASS FUNCTIONS WITH CLR PROPERTY

  • Ghemam Hamed Laid (Dynamic Systems and Control Laboratory, Department of Mathematics, Larbi Ben Mhidi University) ;
  • Iqbal M. Batiha (Department of Mathematics, Faculty of Science and Information Technology, Al Zaytoonah University) ;
  • Leila Benaoua (Dynamic Systems and Control Laboratory, Department of Mathematics, Larbi Ben Mhidi University) ;
  • Taki Eddine Oussaeif (Dynamic Systems and Control Laboratory, Department of Mathematics, Larbi Ben Mhidi University) ;
  • Besma Laouadi (Dynamic Systems and Control Laboratory, Department of Mathematics, Larbi Ben Mhidi University) ;
  • Iqbal H. Jebril (Department of Mathematics, Faculty of Science and Information Technology, Al Zaytoonah University)
  • 투고 : 2023.12.09
  • 심사 : 2024.03.12
  • 발행 : 2024.09.15

초록

The objective of this paper is to ascertain the existence and uniqueness of common fixed point for four self mappings in intuitionistic Menger metric spaces under some conditions extending to (CLR) property and C-class functions. Some illustrative examples are furnished, which demonstrate the validity of the hypotheses. As an application to our main result, we derive a common fixed point theorem for four self-mappings in metric space. Our results generalize several works, including [4], [20].

키워드

참고문헌

  1. A. Abdelhalim, A. Aliouche, L. Benaoua and T.E. Ousseif, Common coupled fixed point theorems for two pairs of weakly compatible mappings in Menger metric spaces, Moroccan J. Pure Appl. Anal., 5(2) (2019), 197-221. 
  2. N.R. Anakira, Adel Almalki, D. Katatbeh, G.B. Hani, A.F. Jameel, Khamis S. Al Kalbani and M. Abu-Dawas, An Algorithm for Solving Linear and Non-Linear Volterra Integro-Differential Equations, Int. J. Adv. Soft Comput. Appl., 15(3) (2023), 69-83. 
  3. A.H. Ansari and A. Mutlu, C-class functions on coupled fixed point theorem for mixed monotone mappings on partial ordered dislocated quasi metric spaces, Nonlinear Funct. Anal. Appl., 22 (1) (2017), 99-106. 
  4. A.H. Ansari, V. Popa, Y.M. Singh and M.S. Khan, Fixed point theorems of an implicit relation via C- class function in metric spaces, J. Adv. Math. Stud., 13(1) (2020), 1-10. 
  5. L. Benaoua and A. Aliouche, A common coupled fixed point theorem in intuitionistic Menger metric space, Mathematica Moravica, 20(2) (2016), 59-85. 
  6. L. Benaoua and A. Aliouche, Coupled fixed point theorems for weakly compatible mappings along with CLR property in Menger metric spaces, Carpathian Math. Publ., 8(2) (2016), 195-210. 
  7. L. Benaoua and A. Aliouche, Common fixed point theorems in intuitionistic Menger space using property EA and an application to Fredholm integral equations, J. Interdisciplinary Math., 25(1) (2022), 1-21. 
  8. L. Benaoua, V. Parvaneh, T. Oussaeif, L. Guran, G.H. Laid and C. Park, Common fixed point theorems in intuitionistic fuzzy metric spaces with an application for Volterra integral equations, Comm. Nonlinear Sci. Numer. Simu., 127 (2023), 107524. 
  9. G. Farraj, M. Banan, K. Rushdi and B. Wahiba, An algorithm for solving fractional differential equations using conformable optimized decomposition method, Int. J. Adv. Soft Comput. Appl., 15(1) (2023), 187-196. 
  10. O. Hadzic and E. Pap, Fixed point theory in probabilistic metric spaces, Springer Science and Business Media, 536, 2001. 
  11. M. Imdad, S. Chauhan and Z. Kadelburg, Fixed point theorems for mappings with common limit range property satisfying generalized (ψ, ϕ)-weak contractive conditions, Math. Sci., Springer, 7 (2013), 1-8. 
  12. M. Imdad, B.D. Pant and S. Chauhan, Fixed point theorems in Menger spaces using the (CLRST ) property and applications, J. Nonlinear Anal. Optim., 3 (2012), 225-237. 
  13. G. Jungck and B.E. Rhoades, Fixed point for set valued functions without continuity, Indian J. Pure Appl. Math., 3 (1998), 227-238. 
  14. S. Kutukcu, On intuitionistic Menger spaces, Bull. Math. Statistics Research, 6 (2018), 28-32. 
  15. B. Laouadi, T.E. Oussaeif, L. Benaoua, L. Guran and S. Radenovic, Some new fixed point results in b-metric space with rational generalized contractive condition, J. Sib. Fed. Univ. Math. Phys., 16(4) (2023), 506518. 
  16. K. Menger, Statistical Metrics, Proc. Nat. Acad. Sci. USA, 28(12) (1942), 535-537. 
  17. B.D. Pant, S. Chauhan and V. Pant, Common fixed point theorems in intuitionistic Menger spaces, J. Adv. Studies Top., 1 (2010), 54-57. 
  18. H. Qawaqneh, Fractional analytic solutions and fixed point results with some applications, Adv. Fixed Point Theory, 14(1) (2024), 1-14. 
  19. N. Saleem, A.H. Ansari and M.K. Jain, Some fixed point theorems of inverse C-class function under weak semi-compatibility, J. Fixed Point Theory, 9 (2018). 
  20. R. Sharma and A.H. Ansari, Some fixed point theorems in an intuitionistic Menger space via C-class and inverse C-class functions, Comput. Math. Meth., 2 (2020), https://doi.org/10.1002/cmm4.1090. 
  21. A. Sharma, A. Jain and S. Choudhari, Sub-compatibility and fixed point theorem in intuitionistic Menger space, Int. J. Theory and Appl. Sci., 3 (2011), 9-12. 
  22. S.L. Singh, B.D. Pant and S. Chauhan, Fixed point theorems in non-Archimedean Menger PM spaces, J. Nonlinear Anal. Optim., 3 (2012), 153-160. 
  23. W. Sintunavarat and P. Kumam, Common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces, J. Appl. Math., (2011), https://doi.org/10.1155/2011/637958.