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Common Fixed Point Theorems Satisfying Implicit Relations on 2-cone Banach Space with an Application

Year 2019, Volume: 7 Issue: 1, 9 - 18, 30.04.2019
https://doi.org/10.36753/mathenot.559237

Abstract

In this paper, we discuss the existence and uniqueness of common fixed-point theorems satisfying implicit

relations on 2-cone Banach spaces. Modifying obtained new contractive conditions, we also give an

application to the fixed-circle problem.

References

  • [1] Abdeljawad, T., Karapınar, E. and Ta¸s, K., Common fixed point theorem in cone Banach space. Hacet. J. Math. Stat. 40 (2011), no. 2, 211-217.
  • [2] Gujetiya, R. K., Mali, D. K. and Hakwadiya, M., Common fixed point theorem for compatible mapping on cone Banach space. Int. J. Math. Anal. 8 (2014), no. 35, 1697-1706.
  • [3] Huang, L. G. and Zhang, X., Cone metric spaces and fixed point theorems of contractive mappings. J. Math. Anal. Appl. 332 (2007), 1468-1476.
  • [4] Karapınar, E., Fixed point theorems in cone Banach spaces. Fixed Point Theory Appl. 2009, Article ID 609281, 9 pages. doi:10.1155/2009/609281.
  • [5] Krishnakumar, R. and Dhamodharan, D., Common fixed point of contractive modulus on 2-cone Banach space. Malaya J. Mat. 5 (2017), no. 3, 608-618.
  • [6] Mlaiki, N., Çelik, U., Ta¸s, N., Özgür, N. Y. and Mukheimer, A.,Wardowski type contractions and the fixed-circle problem on S-metric spaces. J. Math. 2018, Art. ID 9127486, 9 pp.
  • [7] Mlaiki, N., Ta¸s, N. and Özgür, N. Y., On the fixed-circle problem and Khan type contractions. Axioms 7 (2018), 80.
  • [8] Özgür, N. Y. and Ta¸s, N., Some fixed-circle theorems on metric spaces. Bull. Malays. Math. Sci. Soc. (2017). https://doi.org/10.1007/s40840-017-0555-z
  • [9] Özgür, N. Y. and Ta¸s, N., Fixed-circle problem on S-metric spaces with a geometric viewpoint. arXiv:1704.08838 [10] Özgür, N. Y., Ta¸s, N. and Çelik, U., New fixed-circle results on S-metric spaces. Bull. Math. Anal. Appl. 9 (2017), no. 2, 10-23.
  • [11] Özgür, N. Y. and Ta¸s, N., Some fixed-circle theorems and discontinuity at fixed circle. AIP Conference Proceedings, 1926, 020048 (2018).
  • [12] Özgür, N. Y., Fixed-disc results via simulation functions. arXiv:1901.02623
  • [13] Pant, R. P., Özgür, N. Y. and Ta¸s, N., On discontinuity problem at fixed point. Bull. Malays. Math. Sci. Soc. (2018). https://doi.org/10.1007/s40840-018-0698-6.
  • [14] Pitchaimani, M. and Ramesh Kumar, D., Some common fixed point theorems using implicit relation in 2-Banach spaces. Surv. Math. Appl. 10 (2015), 159-168.
  • [15] Rada, E. and Tato, A., An extension of a fixed point result in cone Banach space. Pure and Applied Mathematics Journal 4 (2015), no. 3, 70-74.
  • [16] ¸Sahiner, A. and Yi ˘ git, T., 2-cone Banach spaces and fixed point theorem. Numerical Analysis and Applied Mathematics ICNAAM 2012 AIP Conf. Proc. 1479 (2012), 975-978. doi: 10.1063/1.4756305
  • [17] ¸Sahiner, A., Fixed point theorems in symmetric 2-cone Banach space (lp; k; :; kc p). J. Nonlinear Anal. Optim. 3(2012), no. 2, 115-120.
  • [18] Taş, N., Suzuki-Berinde type fixed-point and fixed-circle results on S-metric spaces. J. Linear Topol. Algebra 7 (2018), no. 3, 233-244.
  • [19]Taş, N., Various types of fixed-point theorems on S-metric spaces. J. BAUN Inst. Sci. Technol. 20 (2018), no. 2, 211-223.
  • [20] Taş, N., Özgür, N. Y. and Mlaiki, N., New types of FC-contractions and the fixed-circle problem. Mathematics 6 (2018), no. 10, 188.
  • [21] Taş, N. and Özgür, N. Y., Some fixed-point results on parametric Nb-metric spaces. Commun. Korean Math. Soc. 33 (2018), no. 3, 943-960.
Year 2019, Volume: 7 Issue: 1, 9 - 18, 30.04.2019
https://doi.org/10.36753/mathenot.559237

Abstract

References

  • [1] Abdeljawad, T., Karapınar, E. and Ta¸s, K., Common fixed point theorem in cone Banach space. Hacet. J. Math. Stat. 40 (2011), no. 2, 211-217.
  • [2] Gujetiya, R. K., Mali, D. K. and Hakwadiya, M., Common fixed point theorem for compatible mapping on cone Banach space. Int. J. Math. Anal. 8 (2014), no. 35, 1697-1706.
  • [3] Huang, L. G. and Zhang, X., Cone metric spaces and fixed point theorems of contractive mappings. J. Math. Anal. Appl. 332 (2007), 1468-1476.
  • [4] Karapınar, E., Fixed point theorems in cone Banach spaces. Fixed Point Theory Appl. 2009, Article ID 609281, 9 pages. doi:10.1155/2009/609281.
  • [5] Krishnakumar, R. and Dhamodharan, D., Common fixed point of contractive modulus on 2-cone Banach space. Malaya J. Mat. 5 (2017), no. 3, 608-618.
  • [6] Mlaiki, N., Çelik, U., Ta¸s, N., Özgür, N. Y. and Mukheimer, A.,Wardowski type contractions and the fixed-circle problem on S-metric spaces. J. Math. 2018, Art. ID 9127486, 9 pp.
  • [7] Mlaiki, N., Ta¸s, N. and Özgür, N. Y., On the fixed-circle problem and Khan type contractions. Axioms 7 (2018), 80.
  • [8] Özgür, N. Y. and Ta¸s, N., Some fixed-circle theorems on metric spaces. Bull. Malays. Math. Sci. Soc. (2017). https://doi.org/10.1007/s40840-017-0555-z
  • [9] Özgür, N. Y. and Ta¸s, N., Fixed-circle problem on S-metric spaces with a geometric viewpoint. arXiv:1704.08838 [10] Özgür, N. Y., Ta¸s, N. and Çelik, U., New fixed-circle results on S-metric spaces. Bull. Math. Anal. Appl. 9 (2017), no. 2, 10-23.
  • [11] Özgür, N. Y. and Ta¸s, N., Some fixed-circle theorems and discontinuity at fixed circle. AIP Conference Proceedings, 1926, 020048 (2018).
  • [12] Özgür, N. Y., Fixed-disc results via simulation functions. arXiv:1901.02623
  • [13] Pant, R. P., Özgür, N. Y. and Ta¸s, N., On discontinuity problem at fixed point. Bull. Malays. Math. Sci. Soc. (2018). https://doi.org/10.1007/s40840-018-0698-6.
  • [14] Pitchaimani, M. and Ramesh Kumar, D., Some common fixed point theorems using implicit relation in 2-Banach spaces. Surv. Math. Appl. 10 (2015), 159-168.
  • [15] Rada, E. and Tato, A., An extension of a fixed point result in cone Banach space. Pure and Applied Mathematics Journal 4 (2015), no. 3, 70-74.
  • [16] ¸Sahiner, A. and Yi ˘ git, T., 2-cone Banach spaces and fixed point theorem. Numerical Analysis and Applied Mathematics ICNAAM 2012 AIP Conf. Proc. 1479 (2012), 975-978. doi: 10.1063/1.4756305
  • [17] ¸Sahiner, A., Fixed point theorems in symmetric 2-cone Banach space (lp; k; :; kc p). J. Nonlinear Anal. Optim. 3(2012), no. 2, 115-120.
  • [18] Taş, N., Suzuki-Berinde type fixed-point and fixed-circle results on S-metric spaces. J. Linear Topol. Algebra 7 (2018), no. 3, 233-244.
  • [19]Taş, N., Various types of fixed-point theorems on S-metric spaces. J. BAUN Inst. Sci. Technol. 20 (2018), no. 2, 211-223.
  • [20] Taş, N., Özgür, N. Y. and Mlaiki, N., New types of FC-contractions and the fixed-circle problem. Mathematics 6 (2018), no. 10, 188.
  • [21] Taş, N. and Özgür, N. Y., Some fixed-point results on parametric Nb-metric spaces. Commun. Korean Math. Soc. 33 (2018), no. 3, 943-960.
There are 20 citations in total.

Details

Primary Language English
Journal Section Articles
Authors

D. Dhamodharan This is me

Nihal Taş This is me

R. Krishnakumar This is me

Publication Date April 30, 2019
Submission Date January 24, 2019
Published in Issue Year 2019 Volume: 7 Issue: 1

Cite

APA Dhamodharan, D., Taş, N., & Krishnakumar, R. (2019). Common Fixed Point Theorems Satisfying Implicit Relations on 2-cone Banach Space with an Application. Mathematical Sciences and Applications E-Notes, 7(1), 9-18. https://doi.org/10.36753/mathenot.559237
AMA Dhamodharan D, Taş N, Krishnakumar R. Common Fixed Point Theorems Satisfying Implicit Relations on 2-cone Banach Space with an Application. Math. Sci. Appl. E-Notes. April 2019;7(1):9-18. doi:10.36753/mathenot.559237
Chicago Dhamodharan, D., Nihal Taş, and R. Krishnakumar. “Common Fixed Point Theorems Satisfying Implicit Relations on 2-Cone Banach Space With an Application”. Mathematical Sciences and Applications E-Notes 7, no. 1 (April 2019): 9-18. https://doi.org/10.36753/mathenot.559237.
EndNote Dhamodharan D, Taş N, Krishnakumar R (April 1, 2019) Common Fixed Point Theorems Satisfying Implicit Relations on 2-cone Banach Space with an Application. Mathematical Sciences and Applications E-Notes 7 1 9–18.
IEEE D. Dhamodharan, N. Taş, and R. Krishnakumar, “Common Fixed Point Theorems Satisfying Implicit Relations on 2-cone Banach Space with an Application”, Math. Sci. Appl. E-Notes, vol. 7, no. 1, pp. 9–18, 2019, doi: 10.36753/mathenot.559237.
ISNAD Dhamodharan, D. et al. “Common Fixed Point Theorems Satisfying Implicit Relations on 2-Cone Banach Space With an Application”. Mathematical Sciences and Applications E-Notes 7/1 (April 2019), 9-18. https://doi.org/10.36753/mathenot.559237.
JAMA Dhamodharan D, Taş N, Krishnakumar R. Common Fixed Point Theorems Satisfying Implicit Relations on 2-cone Banach Space with an Application. Math. Sci. Appl. E-Notes. 2019;7:9–18.
MLA Dhamodharan, D. et al. “Common Fixed Point Theorems Satisfying Implicit Relations on 2-Cone Banach Space With an Application”. Mathematical Sciences and Applications E-Notes, vol. 7, no. 1, 2019, pp. 9-18, doi:10.36753/mathenot.559237.
Vancouver Dhamodharan D, Taş N, Krishnakumar R. Common Fixed Point Theorems Satisfying Implicit Relations on 2-cone Banach Space with an Application. Math. Sci. Appl. E-Notes. 2019;7(1):9-18.

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