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Some fixed point theorems on orthogonal metric spaces via extensions of orthogonal contractions

Year 2022, Volume: 71 Issue: 2, 481 - 489, 30.06.2022
https://doi.org/10.31801/cfsuasmas.970219

Abstract

Orthogonal metric space is a considerable generalization of a usual metric space obtained by establishing a perpendicular relation on a set. Very recently, the notions of orthogonality of the set and orthogonality of the metric space are described and notable fixed point theorems are given in orthogonal metric spaces. Some fixed point theorems for the generalizations of contraction principle via altering distance functions on orthogonal metric spaces are presented and proved in this paper. Furthermore, an example is presented to clarify these theorems.

References

  • Alber, Y. I., Guerre-Delabriere, S., Principle of Weakly Contractive Maps in Hilbert Spaces, In: New Results in Operator Theory and Its Applications, (pp. 7-22) Birkhuser, Basel, 1997.
  • Altun, I., Damjanovic, B., Djoric, D., Fixed point and common fixed point theorems on ordered cone metric spaces, Applied Mathematics Letters, 23(3) (2010), 310-316. https://doi.org/10.1016/j.aml.2009.09.016
  • Banach, S., Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fund. Math., 3 (1922), 133-181.
  • Ciric, L., Damjanovic, B., Jleli, M., Samet, B., Coupled fixed point theorems for generalized Mizoguchi-Takahashi contractions with applications, Fixed Point Theory and Applications, 2012(51) (2012), 1-13. https://doi.org/10.1186/1687-1812-2012-51
  • Debnath, P., Srivastava, H. M., New extensions of Kannan’s and Reich’s fixed point theorems for multivalued maps using Wardowski’s technique with application to integral equations, Symmetry, 12(7) (2020), 1090. https://doi.org/10.3390/sym12071090
  • Debnath, P., Srivastava, H. M., Global optimization and common best proximity points for some multivalued contractive pairs of mappings, Axioms, 9(3) (2020), 102. https://doi.org/10.3390/axioms9030102
  • Debnath, P., De La Sen, M., Contractive inequalities for some asymptotically regular set-valued mappings and their fixed points, Symmetry, 12(3) (2020), 411. https://doi.org/10.3390/sym12030411
  • Debnath, P., Set-valued Meir-Keeler, Geraghty and Edelstein type fixed point results in b-metric spaces, Rendiconti del Circolo Matematico di Palermo Series 2, 70(3) (2021), 1389-1398. https://doi.org/10.1007/s12215-020-00561-y
  • Debnath, P., Neog, M., Radenovic, S., Set valued Reich type G-contractions in a complete metric space with graph, Rendiconti del Circolo Matematico di Palermo Series 2, 69(3) (2020), 917-924. https://doi.org/10.1007/s12215-019-00446-9
  • Debnath, P., Choudhury, B. S., Neog, M., Fixed set of set valued mappings with set valued domain in terms of start set on a metric space with a graph, Fixed Point Theory and Applications, 2017(1) (2016), 1-8. https://doi.org/10.1186/s13663-017-0598-8
  • Debnath, P., Optimization through best proximity points for multivalued F-contractions, Miskolc Mathematical Notes, 22(1) (2021), 143-151. https://doi.org/10.18514/MMN.2021.3355
  • Eshaghi Gordji, M., Habibi, H., Fixed point theory in generalized orthogonal metric space, Journal of Linear and Topological Algebra , 6(3) (2017), 251-260.
  • Gordji, M. E., Ramezani, M., De La Sen, M., Cho, Y. J., On orthogonal sets and Banach fixed point theorem, Fixed Point Theory, 18(2) (2017), 569-578. https://doi.org/10.24193/fptro.2017.2.45
  • Gungor, N. B., Turkoglu, D., Fixed point theorems on orthogonal metric spaces via altering distance functions, In AIP Conference Proceedings, 2183(1) (2019), p. 040011. AIP Publishing. https://doi.org/10.1063/1.5136131
  • Khan, M. S., Swaleh, M., Sessa, S., Fixed point theorems by altering distances between the points, Bulletin of the Australian Mathematical Society, 30(1) (1984), 1-9. https://doi.org/10.1017/S0004972700001659
  • Mehmood, M., Aydi, H., Ali, M. U., Shoaib, A., De La Sen, M., Solutions of integral equations via fixed-point results on orthogonal gauge structure, Mathematical Problems in Engineering, 2021 (2021). https://doi.org/10.1155/2021/8387262
  • Mehmood M., Isik H., Uddin F., Shoaib A., New fixed point theorems for orthogonal contractions in incomplete metric spaces, Carpathian Math.Publ., 2021(13) (2021), 405-412. https://doi.org/10.15330/cmp.13.2.405-412
  • Neog, M., Debnath, P., Radenovic, S., New extension of some common fixed point theorems in complete metric spaces, Fixed Point Theory, 20(2) (2019), 567-580.
  • Rhoades, B. E., Some theorems on weakly contractive maps, Nonlinear Analysis: Theory, Methods and Applications, 47(4) (2001), 2683-2693. https://doi.org/10.1016/S0362-546X(01)00388-1
Year 2022, Volume: 71 Issue: 2, 481 - 489, 30.06.2022
https://doi.org/10.31801/cfsuasmas.970219

Abstract

References

  • Alber, Y. I., Guerre-Delabriere, S., Principle of Weakly Contractive Maps in Hilbert Spaces, In: New Results in Operator Theory and Its Applications, (pp. 7-22) Birkhuser, Basel, 1997.
  • Altun, I., Damjanovic, B., Djoric, D., Fixed point and common fixed point theorems on ordered cone metric spaces, Applied Mathematics Letters, 23(3) (2010), 310-316. https://doi.org/10.1016/j.aml.2009.09.016
  • Banach, S., Sur les operations dans les ensembles abstraits et leur application aux equations integrales, Fund. Math., 3 (1922), 133-181.
  • Ciric, L., Damjanovic, B., Jleli, M., Samet, B., Coupled fixed point theorems for generalized Mizoguchi-Takahashi contractions with applications, Fixed Point Theory and Applications, 2012(51) (2012), 1-13. https://doi.org/10.1186/1687-1812-2012-51
  • Debnath, P., Srivastava, H. M., New extensions of Kannan’s and Reich’s fixed point theorems for multivalued maps using Wardowski’s technique with application to integral equations, Symmetry, 12(7) (2020), 1090. https://doi.org/10.3390/sym12071090
  • Debnath, P., Srivastava, H. M., Global optimization and common best proximity points for some multivalued contractive pairs of mappings, Axioms, 9(3) (2020), 102. https://doi.org/10.3390/axioms9030102
  • Debnath, P., De La Sen, M., Contractive inequalities for some asymptotically regular set-valued mappings and their fixed points, Symmetry, 12(3) (2020), 411. https://doi.org/10.3390/sym12030411
  • Debnath, P., Set-valued Meir-Keeler, Geraghty and Edelstein type fixed point results in b-metric spaces, Rendiconti del Circolo Matematico di Palermo Series 2, 70(3) (2021), 1389-1398. https://doi.org/10.1007/s12215-020-00561-y
  • Debnath, P., Neog, M., Radenovic, S., Set valued Reich type G-contractions in a complete metric space with graph, Rendiconti del Circolo Matematico di Palermo Series 2, 69(3) (2020), 917-924. https://doi.org/10.1007/s12215-019-00446-9
  • Debnath, P., Choudhury, B. S., Neog, M., Fixed set of set valued mappings with set valued domain in terms of start set on a metric space with a graph, Fixed Point Theory and Applications, 2017(1) (2016), 1-8. https://doi.org/10.1186/s13663-017-0598-8
  • Debnath, P., Optimization through best proximity points for multivalued F-contractions, Miskolc Mathematical Notes, 22(1) (2021), 143-151. https://doi.org/10.18514/MMN.2021.3355
  • Eshaghi Gordji, M., Habibi, H., Fixed point theory in generalized orthogonal metric space, Journal of Linear and Topological Algebra , 6(3) (2017), 251-260.
  • Gordji, M. E., Ramezani, M., De La Sen, M., Cho, Y. J., On orthogonal sets and Banach fixed point theorem, Fixed Point Theory, 18(2) (2017), 569-578. https://doi.org/10.24193/fptro.2017.2.45
  • Gungor, N. B., Turkoglu, D., Fixed point theorems on orthogonal metric spaces via altering distance functions, In AIP Conference Proceedings, 2183(1) (2019), p. 040011. AIP Publishing. https://doi.org/10.1063/1.5136131
  • Khan, M. S., Swaleh, M., Sessa, S., Fixed point theorems by altering distances between the points, Bulletin of the Australian Mathematical Society, 30(1) (1984), 1-9. https://doi.org/10.1017/S0004972700001659
  • Mehmood, M., Aydi, H., Ali, M. U., Shoaib, A., De La Sen, M., Solutions of integral equations via fixed-point results on orthogonal gauge structure, Mathematical Problems in Engineering, 2021 (2021). https://doi.org/10.1155/2021/8387262
  • Mehmood M., Isik H., Uddin F., Shoaib A., New fixed point theorems for orthogonal contractions in incomplete metric spaces, Carpathian Math.Publ., 2021(13) (2021), 405-412. https://doi.org/10.15330/cmp.13.2.405-412
  • Neog, M., Debnath, P., Radenovic, S., New extension of some common fixed point theorems in complete metric spaces, Fixed Point Theory, 20(2) (2019), 567-580.
  • Rhoades, B. E., Some theorems on weakly contractive maps, Nonlinear Analysis: Theory, Methods and Applications, 47(4) (2001), 2683-2693. https://doi.org/10.1016/S0362-546X(01)00388-1
There are 19 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Nurcan Bilgili Güngör 0000-0001-5069-5881

Publication Date June 30, 2022
Submission Date July 12, 2021
Acceptance Date November 11, 2021
Published in Issue Year 2022 Volume: 71 Issue: 2

Cite

APA Bilgili Güngör, N. (2022). Some fixed point theorems on orthogonal metric spaces via extensions of orthogonal contractions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 71(2), 481-489. https://doi.org/10.31801/cfsuasmas.970219
AMA Bilgili Güngör N. Some fixed point theorems on orthogonal metric spaces via extensions of orthogonal contractions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. June 2022;71(2):481-489. doi:10.31801/cfsuasmas.970219
Chicago Bilgili Güngör, Nurcan. “Some Fixed Point Theorems on Orthogonal Metric Spaces via Extensions of Orthogonal Contractions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71, no. 2 (June 2022): 481-89. https://doi.org/10.31801/cfsuasmas.970219.
EndNote Bilgili Güngör N (June 1, 2022) Some fixed point theorems on orthogonal metric spaces via extensions of orthogonal contractions. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71 2 481–489.
IEEE N. Bilgili Güngör, “Some fixed point theorems on orthogonal metric spaces via extensions of orthogonal contractions”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 71, no. 2, pp. 481–489, 2022, doi: 10.31801/cfsuasmas.970219.
ISNAD Bilgili Güngör, Nurcan. “Some Fixed Point Theorems on Orthogonal Metric Spaces via Extensions of Orthogonal Contractions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 71/2 (June 2022), 481-489. https://doi.org/10.31801/cfsuasmas.970219.
JAMA Bilgili Güngör N. Some fixed point theorems on orthogonal metric spaces via extensions of orthogonal contractions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71:481–489.
MLA Bilgili Güngör, Nurcan. “Some Fixed Point Theorems on Orthogonal Metric Spaces via Extensions of Orthogonal Contractions”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 71, no. 2, 2022, pp. 481-9, doi:10.31801/cfsuasmas.970219.
Vancouver Bilgili Güngör N. Some fixed point theorems on orthogonal metric spaces via extensions of orthogonal contractions. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2022;71(2):481-9.

Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics.

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