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SOME FIXED POINT THEOREMS FOR WEAKLY PICARD OPERATORS IN COMPLETE METRIC SPACES AND APPLICATIONS

  • Hieu, Doan Trong (Faculty of Basic Sciences Quang Ninh University of Industry) ;
  • Hung, Bui The (Department of Mathematics Thai Nguyen University of Education)
  • Received : 2020.11.01
  • Accepted : 2021.08.26
  • Published : 2022.01.31

Abstract

In this paper, we prove new fixed point theorems for single-valued and multi-valued weakly Picard operators in complete metric spaces and give several examples. As applications, we give several results to Fredholm integral equation.

Keywords

References

  1. S. Antal and U. C. Gairola, Common fixed point for generalized multivalued mappings via simulation function in metric spaces, Commun. Korean Math. Soc. 35 (2020), no. 4, 1107-1121. https://doi.org/10.4134/CKMS.c190388
  2. M. Berinde and V. Berinde, On a general class of multi-valued weakly Picard mappings, J. Math. Anal. Appl. 326 (2007), no. 2, 772-782. https://doi.org/10.1016/j.jmaa.2006.03.016
  3. J. Caristi, Fixed point theorems for mappings satisfying inwardness conditions, Trans. Amer. Math. Soc. 215 (1976), 241-251. https://doi.org/10.2307/1999724
  4. Lj. B. Ciric, A generalization of Banach's contraction principle, Proc. Amer. Math. Soc. 45 (1974), 267-273. https://doi.org/10.2307/2040075
  5. L.-G. Huang and X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl. 332 (2007), no. 2, 1468-1476. https://doi.org/10.1016/j.jmaa.2005.03.087
  6. F. Khojasteh, S. Shukla, and S. Radenovic, A new approach to the study of fixed point theory for simulation functions, Filomat 29 (2015), no. 6, 1189-1194. https://doi.org/10.2298/FIL1506189K
  7. W. A. Kirk, Fixed points of asymptotic contractions, J. Math. Anal. Appl. 277 (2003), no. 2, 645-650. https://doi.org/10.1016/S0022-247X(02)00612-1
  8. S. B. Nadler, Jr., Multi-valued contraction mappings, Pacific J. Math. 30 (1969), 475-488. http://projecteuclid.org/euclid.pjm/1102978504 https://doi.org/10.2140/pjm.1969.30.475
  9. M. Olgun, Bi,cer, and T. Alyildiz, A new aspect to Picard operators with simulation functions, Turkish J. Math. 40 (2016), no. 4, 832-837. https://doi.org/10.3906/mat1505-26
  10. A. Padcharoen, P. Kumam, P. Saipara, and P. Chaipunya, Generalized Suzuki type Zcontraction in complete metric spaces, Kragujevac J. Math. 42 (2018), no. 3, 419-430. https://doi.org/10.5937/kgjmath1803419p
  11. P. V. Subrahmanyam, Remarks on some fixed-point theorems related to Banach's contraction principle, J. Math. Phys. Sci. 8 (1974), 445-457.
  12. T. Suzuki, Generalized distance and existence theorems in complete metric spaces, J. Math. Anal. Appl. 253 (2001), no. 2, 440-458. https://doi.org/10.1006/jmaa.2000.7151
  13. T. Suzuki, A generalized Banach contraction principle that characterizes metric completeness, Proc. Amer. Math. Soc. 136 (2007), 1861-1869. https://doi.org/10.1090/S0002-9939-07-09055-7