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Some Results on Related Fixed Point Theorems in Two $S$-Metric Spaces

Year 2024, , 110 - 117, 29.03.2024
https://doi.org/10.53570/jnt.1443624

Abstract

In this study, by considering the technique in the theorem of Bollenbacher and Hicks, we obtain some related fixed point theorems involving two mappings on two related complete $S$-metric spaces with certain conditions. As the applications of the main theorem, we then derive some new related fixed point theorems involving a pair of mappings in such spaces. We finally discuss the need for further research.

References

  • S. Sedghi, N. Shobe, A. Aliouche, A generalization of fixed point theorems in $S$-metric spaces, Matematički Vesnik 64 (3) (2012) 258-266.
  • S. Sedghi, I. Altun, N. Shobe, M. A. Salahshour, Some properties of $S$-metric spaces and fixed point results, Kyungpook Mathematical Journal 54 (2014) 113-122.
  • S. Sedghi, N. Shobkolaei, M. Shahraki, T. Dǒsenovič, Common fixed point of four maps in S-metric spaces, Mathematical Sciences 12 (2018) 137-143.
  • M. Shahraki, S. Sedghi, S. M. A. Aleomraninejad, Z. D. Mitrović, Some fixed point results on S-metric spaces, Acta Universitatis Sapientiae, Mathematica 12 (2) (2020) 347-357.
  • N. Özgür, N. Taş, A new solution to the Rhodes' open problem with an application, Acta Universitatis Sapientiae, Mathematica 13 (2) (2021) 427-441.
  • V. Popa, A. M. Patriciu, Ageneral common fixed point theorem for a pair of mappings in $S$-metric spaces, General Mathematics 29 (1) (2021) 31-39.
  • V. Popa, A. M. Patriciu, A general fixed point theorem for mappings satisfying a cyclical contractive condition in $S$-metric spaces, Symmetry 13 (2021) 638 7 pages.
  • H. Karayılan, Some results on fixed point of function in $S$-metric spaces, in: I. Zhelezarov (Ed.), International Scientific Conference, Gabrovo, 2023, Vol. II pp. 242-245.
  • B. Fisher, Fixed points on two metric spaces, Glasnik Matematički 16 (36) (1981) 333--337.
  • B. Fisher, Related fixed points on two metric spaces, Mathematics Seminar Notes 10 (1982) 17-26.
  • B. Fisher, P. P. Murthy, Related fixed point theorems for two mappings on two metric spaces, Kyungpook Mathematical Journal 37 (2) (1997) 343-347.
  • B. Fisher, D. Türkoğlu, Related fixed points for set-valued mappings on two metric spaces, International Journal of Mathematics and Mathematical Sciences 23 (3) (2000) 205-210.
  • R. K. Nomdeo, N. K. Tiwari, B. Fisher, K. Taş, Related fixed point theorems on two complete and compact metric spaces, International Journal of Mathematics and Mathematical Sciences 21 (3) (1998) 559-564.
  • V. Popa, A general fixed point theorem for two pairs of mappings on two metric spaces, Novi Sad Journal of Mathematics 35 (2) (2005) 79-83.
  • V. Popa, M. Telci, Fixed point theorems for mappings implicit relations on two metric spaces, Mathematica Balkanica 20 (2) (2006) 143-152.
  • M. Telci, Fixed points on two complete and compact metric spaces, Applied Mathematics and Mechanics 22 (5) (2001) 564-568.
  • M. Telci, Some results on related fixed points, Journal Fixed Point Theory 2019 (2019) 5 13 pages.
  • A. Bollenbacher, T. L. Hicks, A fixed point theorem revisited, Proceedings of the American Mathematical Society 102 (4) (1988) 898-900.
  • L. L. Ćirić, Periodic and fixed point theorems in a quasi-metric space, Journal of the Australian Mathematical Society (Series A) 54 (1) (1993) 80-85.
Year 2024, , 110 - 117, 29.03.2024
https://doi.org/10.53570/jnt.1443624

Abstract

References

  • S. Sedghi, N. Shobe, A. Aliouche, A generalization of fixed point theorems in $S$-metric spaces, Matematički Vesnik 64 (3) (2012) 258-266.
  • S. Sedghi, I. Altun, N. Shobe, M. A. Salahshour, Some properties of $S$-metric spaces and fixed point results, Kyungpook Mathematical Journal 54 (2014) 113-122.
  • S. Sedghi, N. Shobkolaei, M. Shahraki, T. Dǒsenovič, Common fixed point of four maps in S-metric spaces, Mathematical Sciences 12 (2018) 137-143.
  • M. Shahraki, S. Sedghi, S. M. A. Aleomraninejad, Z. D. Mitrović, Some fixed point results on S-metric spaces, Acta Universitatis Sapientiae, Mathematica 12 (2) (2020) 347-357.
  • N. Özgür, N. Taş, A new solution to the Rhodes' open problem with an application, Acta Universitatis Sapientiae, Mathematica 13 (2) (2021) 427-441.
  • V. Popa, A. M. Patriciu, Ageneral common fixed point theorem for a pair of mappings in $S$-metric spaces, General Mathematics 29 (1) (2021) 31-39.
  • V. Popa, A. M. Patriciu, A general fixed point theorem for mappings satisfying a cyclical contractive condition in $S$-metric spaces, Symmetry 13 (2021) 638 7 pages.
  • H. Karayılan, Some results on fixed point of function in $S$-metric spaces, in: I. Zhelezarov (Ed.), International Scientific Conference, Gabrovo, 2023, Vol. II pp. 242-245.
  • B. Fisher, Fixed points on two metric spaces, Glasnik Matematički 16 (36) (1981) 333--337.
  • B. Fisher, Related fixed points on two metric spaces, Mathematics Seminar Notes 10 (1982) 17-26.
  • B. Fisher, P. P. Murthy, Related fixed point theorems for two mappings on two metric spaces, Kyungpook Mathematical Journal 37 (2) (1997) 343-347.
  • B. Fisher, D. Türkoğlu, Related fixed points for set-valued mappings on two metric spaces, International Journal of Mathematics and Mathematical Sciences 23 (3) (2000) 205-210.
  • R. K. Nomdeo, N. K. Tiwari, B. Fisher, K. Taş, Related fixed point theorems on two complete and compact metric spaces, International Journal of Mathematics and Mathematical Sciences 21 (3) (1998) 559-564.
  • V. Popa, A general fixed point theorem for two pairs of mappings on two metric spaces, Novi Sad Journal of Mathematics 35 (2) (2005) 79-83.
  • V. Popa, M. Telci, Fixed point theorems for mappings implicit relations on two metric spaces, Mathematica Balkanica 20 (2) (2006) 143-152.
  • M. Telci, Fixed points on two complete and compact metric spaces, Applied Mathematics and Mechanics 22 (5) (2001) 564-568.
  • M. Telci, Some results on related fixed points, Journal Fixed Point Theory 2019 (2019) 5 13 pages.
  • A. Bollenbacher, T. L. Hicks, A fixed point theorem revisited, Proceedings of the American Mathematical Society 102 (4) (1988) 898-900.
  • L. L. Ćirić, Periodic and fixed point theorems in a quasi-metric space, Journal of the Australian Mathematical Society (Series A) 54 (1) (1993) 80-85.
There are 19 citations in total.

Details

Primary Language English
Subjects Operator Algebras and Functional Analysis
Journal Section Research Article
Authors

Hakan Karayılan 0000-0002-0266-8106

Early Pub Date March 28, 2024
Publication Date March 29, 2024
Submission Date February 27, 2024
Acceptance Date March 22, 2024
Published in Issue Year 2024

Cite

APA Karayılan, H. (2024). Some Results on Related Fixed Point Theorems in Two $S$-Metric Spaces. Journal of New Theory(46), 110-117. https://doi.org/10.53570/jnt.1443624
AMA Karayılan H. Some Results on Related Fixed Point Theorems in Two $S$-Metric Spaces. JNT. March 2024;(46):110-117. doi:10.53570/jnt.1443624
Chicago Karayılan, Hakan. “Some Results on Related Fixed Point Theorems in Two $S$-Metric Spaces”. Journal of New Theory, no. 46 (March 2024): 110-17. https://doi.org/10.53570/jnt.1443624.
EndNote Karayılan H (March 1, 2024) Some Results on Related Fixed Point Theorems in Two $S$-Metric Spaces. Journal of New Theory 46 110–117.
IEEE H. Karayılan, “Some Results on Related Fixed Point Theorems in Two $S$-Metric Spaces”, JNT, no. 46, pp. 110–117, March 2024, doi: 10.53570/jnt.1443624.
ISNAD Karayılan, Hakan. “Some Results on Related Fixed Point Theorems in Two $S$-Metric Spaces”. Journal of New Theory 46 (March 2024), 110-117. https://doi.org/10.53570/jnt.1443624.
JAMA Karayılan H. Some Results on Related Fixed Point Theorems in Two $S$-Metric Spaces. JNT. 2024;:110–117.
MLA Karayılan, Hakan. “Some Results on Related Fixed Point Theorems in Two $S$-Metric Spaces”. Journal of New Theory, no. 46, 2024, pp. 110-7, doi:10.53570/jnt.1443624.
Vancouver Karayılan H. Some Results on Related Fixed Point Theorems in Two $S$-Metric Spaces. JNT. 2024(46):110-7.


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