Nonlinear Functional Analysis and Applications

Kyungnam University, Department of Mathematics Eduaction (경남대학교 수학교육과)
권호 표지
DOI QR코드

DOI QR Code

SOME COINCIDENCE POINT THEOREMS FOR PREŠIĆ-ĆIRIĆ TYPE CONTRACTIONS

  • Khan, Qamrul Haq (Department of Mathematics, Faculty of Science Aligarh Muslim University) ;
  • Sk, Faruk (Department of Mathematics, Faculty of Science Aligarh Muslim University)
  • Received : 2020.09.18
  • Accepted : 2020.12.24
  • Published : 2021.12.15
Download PDF
⟨ Previous Next ⟩

Abstract

In this paper, we prove some coincidence point theorems for mappings satisfying nonlinear Prešić-Ćirić type contraction in complete metric spaces as well as in ordered metric spaces. As a consequence, we deduce corresponding fixed point theorems. Further, we give some examples to substantiate the utility of our results.

Keywords

Acknowledgement

The authors are grateful to the anonymous referees for their valuable comments and suggestions which improve the paper.

References

  1. A. Alam, Q.H. Khan and M. Imdad, Enriching the recent coincidence theorem for nonlinear contraction in ordered metric spaces, Fixed point theory Appl., 2015, 141 (2015), 1-14. https://doi.org/10.1186/1687-1812-2015-1
  2. A. Alam, Q.H. Khan and M.Imdad, Discussion on some recent order-theoretic metrical coincidence theorems involving nonlinear contractions, J. Funct. Spaces, Vol 2016, Article ID 6275367, 1-11.
  3. S. Banach, Sur les operations dans les ensembles abstraits et leur applications aux equations integrales, Fund. Math. 3 (1922), 133-181. https://doi.org/10.4064/fm-3-1-133-181
  4. L.B. Ciric and S.B. Presic, On Presic type generalization of Banach contraction principle, Acta Math. Uni. Com., 76 (2007), 143-147.
  5. R. George, K.P. Freshman and R. Palanquin, A generalized fixed point theorem of Ciric type in cone metric spaces and application to Markov process, Fixed Point Theory Appl., 2011 : 85 (2011) doi 10.1186/1687-1812-2011-85.
  6. R. Kannan, Some results on fixed point, Bull. Calcutta Math. Soc., 60 (1968), 71-76.
  7. Q.H. Khan and T. Rashid, Coupled coincidence point of φ-contraction type T-coupling in partial metric spaces, J. Math. Anal., 8 (2018), 136-149,
  8. N.V. Long and N. Xian Thuan, Some fixed point theorems of Presic-Ciric type, Acts Uni.Plus, 30 (2012), 237-249.
  9. J. Matkowski, Fixed point theorems for mappings with a contractive iterate at a point, Proc. Amer. Math. Soc., 62(2) (1977), 344-348. https://doi.org/10.1090/S0002-9939-1977-0436113-5
  10. S. Malhotra, S. Shukla and S. Sen, A generalization of Banach contraction principle in ordered cone metric spaces, J. Adv. Math. Stud. 5(2) (2012), 59-67.
  11. S.B. Presic, Sur la convergence des suites. (French), C. R. Cad Sci. Paris, 260 (1965), 3828-73830.
  12. S.B. Presic, Sur une classe dinequations aux differences nite et sur la convergence de certaines suites. (French), Publ. Inst. Math. Beograd (N.S.), 19(5) (1965), 75-78.
  13. M. Pacurar, A multi-step iterative method for approximating fixed point of Presic-Kannan operators, Acta. Math. Univ. Comenianae, Vol.LXXIX, 1 (2010), 77-88.
  14. S. Riech, Some remarks concerning contraction mappings, Can. Math. Bull., 14 (1971), 121-124. https://doi.org/10.4153/CMB-1971-024-9
  15. I.A. Rus, An iterative method for the solution of the equation x = f (x,...), Rev. Anal. Numer. Theor. Approx., 10(1) (1981), 95-100.
  16. B.E. Rhoades, A comparison of various definitions of contractive mappings , Trans. Amer. Math. Soc., 226 (1977), 257-290. https://doi.org/10.2307/1997954
  17. T. Rashid, Q.H. Khan and H. Aydi, On Strong coupled coincidence points of g-coupling and an application, J. Funct. Spaces, 2018, Article ID 4034535; 10.
  18. T. Rashid, N. Alharbi, Q.H. Khan, H. Aydi and C. Ozel, Order-Theoretic metrical coincidence theorem involving point (φ, ψ)- Contractions, J. Math. Anal., 9 (2018), 119-135.