Research Article
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Year 2021, Volume: 70 Issue: 2, 690 - 701, 31.12.2021

Kübra Özkan Utku Gürdal Ali Mutlu

https://doi.org/10.31801/cfsuasmas.727771

Abstract

References

  • Abbas, M., Rajic, V. C., Nazir, T., Radenovic, S., Common fixed point of mappings satisfying rational inequalities in ordered complex valued generalized metric spaces, Afrika Matematika, (2013), 1-14. https://doi.org/10.1007/s13370-013-0185-z.
  • Ahmad, J., Klin-eam, C., Azam, A., Common fixed points for multi-valued mappings in complex valued metric spaces with applications, Abstract and applied analysis, 2013 (2013), Article ID 854965, 12 pages. https://doi.org/10.1155/2013/854965.
  • Alaca, C., Ege, M.E., Park, C., Fixed point results for modular ultrametric spaces, Journal of Computational Analysis and Applications, 20(7) (2016), 1259-1267.
  • Ansari, A. H., Ege, Ö., Radenovi´c, S., Some fixed point results on complex valued Gb-metric spaces, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, 112 (4), (2017), doi: 10.1007/s13398-017-0391-x.
  • Asadi, M., Moeini, B., Mukheimer, A., Aydi, H., Complex valued M-metric spaces and related fixed point results via complex C-class function, Journal of Inequalities and Special Functions, 10(1) (2019), 101-110.
  • Azam, A., Fisher B., Khan, M., Common fixed point theorems in complex valued metric spaces, Numerical Functional Analysis and Optimization, 32(3) (2011), 243-253. https://doi.org/10.1080/01630563.2011.533046.
  • Azam, A., Ahmad, J., Kumam, P., Common fixed point theorems for multi-valued mappings in complex-valued metric spaces, Journal of Inequalities and Applications, 2013, 2013:578.
  • Abdou, A. A. N., Khamsi, M. A., On the fixed points of nonexpansive mappings in modular metric spaces, Fixed Point Theory and Applications, (2013), 2013:229. https://doi.org/10.1186/1029-242X-2013-578.
  • Aksoy, U., Karapinar, E., Erhan, M., Rakocevic, V., Meir-Keeler type contractions on modular metric spaces, Filomat, 32(10) (2013), 3697-3707. https://doi.org/10.2298/FIL1810697A.
  • Banach, S., Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fundamenta Mathematicae, 3 (1922), 133-181.
  • Chistyakov, V. V., Modular metric spaces generated by F-modulars, Folia Mathematica, 14 (2008), 3-25.
  • Chistyakov, V. V., Modular metric spaces I basic concepts, Nonlinear Analysis, 72 (2010), 1-14. https://doi.org/10.1016/j.na.2009.04.057.
  • Chistyakov, V. V., Fixed points of modular contractive maps, Doklady Mathematics, 86(1) (2012), 515-518. https://doi.org/10.1134/S1064562412040163.
  • Cho, Y.J., Saadati, R., Sadeghi, G., Quasi-contractive mappings in modular metric spaces, Journal of Applied Mathematics, (2012), Article ID 907951, 5 pages. https://doi.org/10.1155/2012/907951.
  • Humaira, H., Sarwar, M., Kumam, P., Common fixed point results for fuzzy mappings on complex-valued metric spaces with homotopy results, Symmetry, 11(1) (2019), 61; https://doi.org/10.3390/sym11010061.
  • Hussain, N., Ahmad, J., Azam, A., Arshad, M., Common fixed point results in complex valued metric spaces with application to integral equations, Filomat, 28(7) (2014), 1363-1380. https://doi.org/10.2298/FIL1407363H.
  • Ege, M. E., Alaca, C., Fixed point results and an application to homotopy in modular metric spaces, Journal of Nonlinear Science and Applications, 8(6) (2015), 900-908.
  • Ege, M. E., Alaca, C., Some properties of modular S-metric spaces and its fixed point results, Journal of Computational Analysis and Applications, 20(1) (2016), 24-33.
  • Ege, M. E., Alaca, C., Some results for modular b-metric spaces and an application to system of linear equations, Azerbaijan Journal of Mathematics, 8(1) (2018), 3-14.
  • Ege, Ö., Some fixed point theorems in complex valued Gb metric spaces, Journal of Nonlinear and Convex Analysis, 18(11) (2017), 1997-2005.
  • Kilinç, E., Alaca, C., A Fixed point theorem in modular metric spaces, Advances Fixed Point Theory, 4 (2014), 199-206.
  • Kutbi, M. A., Azam, A., Ahmad, J., Di Bari, C., Some common coupled fixed point results for generalized contraction in complex-valued metric spaces, Journal of Applied Mathematics, (2013), 2013: Article ID 352927. https://doi.org/10.1155/2013/352927.
  • Mongkolkeha, C., Sintunavarat, W., Kumam, P., Fixed point theorems for contraction mappings in modular metric spaces, Fixed Point Theory and Applications (2011), 2011:93. https://doi.org/10.1186/1687-1812-2011-93.
  • Kumam, P., Sarwar, M., Zada, M. B., Fixed point results satisfying rational type contractive conditions in complex valued metric spaces, Annales Mathematicae Silesianae, 30 (2016), 89-110. https://doi.org/10.1515/amsil-2016-0003.
  • Mukheimer, A., Common fixed point theorems for a pair of mappings in complex valued b-metric spaces, Advances in Fixed Point Theory, 4(3) (2014), 344-354.
  • Mukheimer, A., Some fixed point theorems in complex valued b-metric spaces, Italian Journal of Pure and Applied Mathematics, 42 (2019), 11-125.
  • Mutlu, A., Özkan, K., Gürdal, U., A new fixed point theorem in modular metric spaces, International Journal of Analysis and Applications, 16(4) (2018), 1-10. https://doi.org/10.28924/2291-8639.
  • Mutlu, A., Özkan, K., Gürdal, U., Coupled fixed point theorem in partially ordered modular metric spaces and its an application, Journal of Computational Analysis and Applications, 25(2) (2018), 1-10.
  • Musielak, J., Orlicz, W., On modular spaces, Studia Mathematica, 18 (1959), 49-65.
  • Nakano, H., Modulared semi-ordered linear spaces, In Tokyo Math. Book Ser., vol. 1, Maruzen Co., Tokyo, 1950.
  • Sarwar, M., Zada, M. B., Manro, S., Common fixed point theorems for weakly compatible mappings in complex valued metric spaces, Bulletin of the International Mathematical Virtual Institute, 7, (2017), 11-21.
  • Sarwar, M., Humaira, H., Li, T., Fuzzy Fixed point results and applications to ordinary fuzzy differential equations in complex valued metric spaces, Hacettepe Journal of Mathematics and Statistics, 48(6) (2019), 1712-1728. https://doi.org/10.15672/HJMS.2018.633.
  • Shatanawi, W., Norani, J. A., Alsamir, H., Kutbi, M. A., Some common fixed points of multivalued mappings on complex-valued metric spaces with homotopy result, Journal of Nonlinear Sciences and Applications, 10 (2017), 3381-3396. https://doi.org/10.22436/JNSA.010.07.02.
  • Sintunavarat, W., Kumam, P., Generalized common fixed point theorems in complex valued metric spaces and applications, Journal of Inequalities and Applications, 2012 (2012), article 84. https://doi.org/10.1186/1029-242X-2012-84.
  • Sunanda, R., Patil, J., Salunke, N., Common fixed point theorems in complex valued rectangular metric spaces, South Asian Journal of Mathematics, 6(1) (2016), 10-23.

Some fixed point theorems on complex valued modular metric spaces with an application

Year 2021, Volume: 70 Issue: 2, 690 - 701, 31.12.2021

Kübra Özkan Utku Gürdal Ali Mutlu

https://doi.org/10.31801/cfsuasmas.727771

Abstract

In this article, we introduce the notion of complex valued modular metric spaces. We also a prove generalization of Banach Fixed Point Theorem, which is one of the most simple and significant tests for existence and uniqueness of solution of problems arising in mathematics and engineering for complex valued modular metric spaces. In addition, we express some results related to these spaces. Finally, we give an application of our results to digital programming.

Keywords

Fixed point complex valued modular metric spaces completeness

References

  • Abbas, M., Rajic, V. C., Nazir, T., Radenovic, S., Common fixed point of mappings satisfying rational inequalities in ordered complex valued generalized metric spaces, Afrika Matematika, (2013), 1-14. https://doi.org/10.1007/s13370-013-0185-z.
  • Ahmad, J., Klin-eam, C., Azam, A., Common fixed points for multi-valued mappings in complex valued metric spaces with applications, Abstract and applied analysis, 2013 (2013), Article ID 854965, 12 pages. https://doi.org/10.1155/2013/854965.
  • Alaca, C., Ege, M.E., Park, C., Fixed point results for modular ultrametric spaces, Journal of Computational Analysis and Applications, 20(7) (2016), 1259-1267.
  • Ansari, A. H., Ege, Ö., Radenovi´c, S., Some fixed point results on complex valued Gb-metric spaces, Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales - Serie A: Matematicas, 112 (4), (2017), doi: 10.1007/s13398-017-0391-x.
  • Asadi, M., Moeini, B., Mukheimer, A., Aydi, H., Complex valued M-metric spaces and related fixed point results via complex C-class function, Journal of Inequalities and Special Functions, 10(1) (2019), 101-110.
  • Azam, A., Fisher B., Khan, M., Common fixed point theorems in complex valued metric spaces, Numerical Functional Analysis and Optimization, 32(3) (2011), 243-253. https://doi.org/10.1080/01630563.2011.533046.
  • Azam, A., Ahmad, J., Kumam, P., Common fixed point theorems for multi-valued mappings in complex-valued metric spaces, Journal of Inequalities and Applications, 2013, 2013:578.
  • Abdou, A. A. N., Khamsi, M. A., On the fixed points of nonexpansive mappings in modular metric spaces, Fixed Point Theory and Applications, (2013), 2013:229. https://doi.org/10.1186/1029-242X-2013-578.
  • Aksoy, U., Karapinar, E., Erhan, M., Rakocevic, V., Meir-Keeler type contractions on modular metric spaces, Filomat, 32(10) (2013), 3697-3707. https://doi.org/10.2298/FIL1810697A.
  • Banach, S., Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fundamenta Mathematicae, 3 (1922), 133-181.
  • Chistyakov, V. V., Modular metric spaces generated by F-modulars, Folia Mathematica, 14 (2008), 3-25.
  • Chistyakov, V. V., Modular metric spaces I basic concepts, Nonlinear Analysis, 72 (2010), 1-14. https://doi.org/10.1016/j.na.2009.04.057.
  • Chistyakov, V. V., Fixed points of modular contractive maps, Doklady Mathematics, 86(1) (2012), 515-518. https://doi.org/10.1134/S1064562412040163.
  • Cho, Y.J., Saadati, R., Sadeghi, G., Quasi-contractive mappings in modular metric spaces, Journal of Applied Mathematics, (2012), Article ID 907951, 5 pages. https://doi.org/10.1155/2012/907951.
  • Humaira, H., Sarwar, M., Kumam, P., Common fixed point results for fuzzy mappings on complex-valued metric spaces with homotopy results, Symmetry, 11(1) (2019), 61; https://doi.org/10.3390/sym11010061.
  • Hussain, N., Ahmad, J., Azam, A., Arshad, M., Common fixed point results in complex valued metric spaces with application to integral equations, Filomat, 28(7) (2014), 1363-1380. https://doi.org/10.2298/FIL1407363H.
  • Ege, M. E., Alaca, C., Fixed point results and an application to homotopy in modular metric spaces, Journal of Nonlinear Science and Applications, 8(6) (2015), 900-908.
  • Ege, M. E., Alaca, C., Some properties of modular S-metric spaces and its fixed point results, Journal of Computational Analysis and Applications, 20(1) (2016), 24-33.
  • Ege, M. E., Alaca, C., Some results for modular b-metric spaces and an application to system of linear equations, Azerbaijan Journal of Mathematics, 8(1) (2018), 3-14.
  • Ege, Ö., Some fixed point theorems in complex valued Gb metric spaces, Journal of Nonlinear and Convex Analysis, 18(11) (2017), 1997-2005.
  • Kilinç, E., Alaca, C., A Fixed point theorem in modular metric spaces, Advances Fixed Point Theory, 4 (2014), 199-206.
  • Kutbi, M. A., Azam, A., Ahmad, J., Di Bari, C., Some common coupled fixed point results for generalized contraction in complex-valued metric spaces, Journal of Applied Mathematics, (2013), 2013: Article ID 352927. https://doi.org/10.1155/2013/352927.
  • Mongkolkeha, C., Sintunavarat, W., Kumam, P., Fixed point theorems for contraction mappings in modular metric spaces, Fixed Point Theory and Applications (2011), 2011:93. https://doi.org/10.1186/1687-1812-2011-93.
  • Kumam, P., Sarwar, M., Zada, M. B., Fixed point results satisfying rational type contractive conditions in complex valued metric spaces, Annales Mathematicae Silesianae, 30 (2016), 89-110. https://doi.org/10.1515/amsil-2016-0003.
  • Mukheimer, A., Common fixed point theorems for a pair of mappings in complex valued b-metric spaces, Advances in Fixed Point Theory, 4(3) (2014), 344-354.
  • Mukheimer, A., Some fixed point theorems in complex valued b-metric spaces, Italian Journal of Pure and Applied Mathematics, 42 (2019), 11-125.
  • Mutlu, A., Özkan, K., Gürdal, U., A new fixed point theorem in modular metric spaces, International Journal of Analysis and Applications, 16(4) (2018), 1-10. https://doi.org/10.28924/2291-8639.
  • Mutlu, A., Özkan, K., Gürdal, U., Coupled fixed point theorem in partially ordered modular metric spaces and its an application, Journal of Computational Analysis and Applications, 25(2) (2018), 1-10.
  • Musielak, J., Orlicz, W., On modular spaces, Studia Mathematica, 18 (1959), 49-65.
  • Nakano, H., Modulared semi-ordered linear spaces, In Tokyo Math. Book Ser., vol. 1, Maruzen Co., Tokyo, 1950.
  • Sarwar, M., Zada, M. B., Manro, S., Common fixed point theorems for weakly compatible mappings in complex valued metric spaces, Bulletin of the International Mathematical Virtual Institute, 7, (2017), 11-21.
  • Sarwar, M., Humaira, H., Li, T., Fuzzy Fixed point results and applications to ordinary fuzzy differential equations in complex valued metric spaces, Hacettepe Journal of Mathematics and Statistics, 48(6) (2019), 1712-1728. https://doi.org/10.15672/HJMS.2018.633.
  • Shatanawi, W., Norani, J. A., Alsamir, H., Kutbi, M. A., Some common fixed points of multivalued mappings on complex-valued metric spaces with homotopy result, Journal of Nonlinear Sciences and Applications, 10 (2017), 3381-3396. https://doi.org/10.22436/JNSA.010.07.02.
  • Sintunavarat, W., Kumam, P., Generalized common fixed point theorems in complex valued metric spaces and applications, Journal of Inequalities and Applications, 2012 (2012), article 84. https://doi.org/10.1186/1029-242X-2012-84.
  • Sunanda, R., Patil, J., Salunke, N., Common fixed point theorems in complex valued rectangular metric spaces, South Asian Journal of Mathematics, 6(1) (2016), 10-23.
There are 35 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Articles
Authors

Kübra Özkan 0000-0002-8014-1713

Utku Gürdal 0000-0003-2887-2188

Ali Mutlu 0000-0002-6963-4381

Publication Date December 31, 2021
Submission Date April 27, 2020
Acceptance Date March 8, 2021
Published in Issue Year 2021 Volume: 70 Issue: 2

Cite

APA Özkan, K., Gürdal, U., & Mutlu, A. (2021). Some fixed point theorems on complex valued modular metric spaces with an application. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, 70(2), 690-701. https://doi.org/10.31801/cfsuasmas.727771
AMA Özkan K, Gürdal U, Mutlu A. Some fixed point theorems on complex valued modular metric spaces with an application. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. December 2021;70(2):690-701. doi:10.31801/cfsuasmas.727771
Chicago Özkan, Kübra, Utku Gürdal, and Ali Mutlu. “Some Fixed Point Theorems on Complex Valued Modular Metric Spaces With an Application”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70, no. 2 (December 2021): 690-701. https://doi.org/10.31801/cfsuasmas.727771.
EndNote Özkan K, Gürdal U, Mutlu A (December 1, 2021) Some fixed point theorems on complex valued modular metric spaces with an application. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70 2 690–701.
IEEE K. Özkan, U. Gürdal, and A. Mutlu, “Some fixed point theorems on complex valued modular metric spaces with an application”, Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat., vol. 70, no. 2, pp. 690–701, 2021, doi: 10.31801/cfsuasmas.727771.
ISNAD Özkan, Kübra et al. “Some Fixed Point Theorems on Complex Valued Modular Metric Spaces With an Application”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics 70/2 (December 2021), 690-701. https://doi.org/10.31801/cfsuasmas.727771.
JAMA Özkan K, Gürdal U, Mutlu A. Some fixed point theorems on complex valued modular metric spaces with an application. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70:690–701.
MLA Özkan, Kübra et al. “Some Fixed Point Theorems on Complex Valued Modular Metric Spaces With an Application”. Communications Faculty of Sciences University of Ankara Series A1 Mathematics and Statistics, vol. 70, no. 2, 2021, pp. 690-01, doi:10.31801/cfsuasmas.727771.
Vancouver Özkan K, Gürdal U, Mutlu A. Some fixed point theorems on complex valued modular metric spaces with an application. Commun. Fac. Sci. Univ. Ank. Ser. A1 Math. Stat. 2021;70(2):690-701.

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

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