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Common fixed point theorems in multiplicative $\mathfrak{m}$-metric space with applications to the system of multiplicative integral equations and numerical results

Yıl 2025, Cilt: 54 Sayı: 3, 822 - 833, 24.06.2025

Kapil Yadav , Deepak Kumar

https://doi.org/10.15672/hujms.1336232

Öz

This paper presents common fixed point results for a pair of self-mappings in multiplicative $\mathfrak{m}$-metric space. Also, we present the multiplicative partial metric structure as a specific case of a multiplicative m-metric space and demonstrate some common fixed point results. To support our conclusions, we present an illustrative example with discontinuous self-mappings. We also provide numerical iterations to approximate the common fixed point and graphs to visually substantiate the results. As the consequences of our results, we demonstrate several common fixed point results in $\mathfrak{m}$-metric space and partial metric space. Our findings generalize various fixed point results from the literature. Furthermore, we employ the results to demonstrate the existence and uniqueness of solutions to a system of multiplicative Fredholm integral equations.

Anahtar Kelimeler

multiplicative metric space $\mathfrak{m}$-metric space multiplicative $\mathfrak{m}$-metric space fixed point

Kaynakça

  • [1] M. Abbas, B. Ali and Y.I. Suleman, Common fixed point of locally contractive mappings in multiplicative metric spaces with application, Int. J. Math. Math. Sci. 2015, 218683, 2015.
  • [2] M. Abbas, M. Da La Sen and T. Nazir, Common fixed point of generalized rational type cocyclic mappings in multiplicative metric space, Discrete Dyn. Nat. Soc. 2015, 532725, 2015.
  • [3] A.A.N. Abdou, Fixed point theorems for generalized contractive mappings in multiplicative metric spaces, J. Nonlinear Sci. Appl. 9 (5), 2347–2363, 2016.
  • [4] M. Asadi, E. Karpinar, and P. Salimi, New extension of p-metric space with some fixed-point results on M-metric spaces, J. Inequal. Appl. 2014, Art. No. 18, 2014.
  • [5] S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math. 3 (1), 133–181, 1922.
  • [6] A.E. Bashirov, E.M. Kurpinar and A. Ozyapici, Multiplicative calculus and its applications, J. Math. Anal. Appl. 337 (1), 36–48, 2008.
  • [7] S.K. Chatterjea, Fixed point theorems, C.R. Acad. Bulgare Sci. 25, 727–730, 1972.
  • [8] M. Grossman and R. Katz, Non-Newtonian Calculus, Lee Press, Pigeon Cove, MA, 1972.
  • [9] X. He, M. Song and D. Chen, Common fixed points for weak commutative mappings on multiplicative metric space, Fixed Point Theory Appl. 2014, Art. No. 48, 2014 .
  • [10] H. Huang, G. Deng, T. Doenovi and N. Hussain, Note on recent common coupled fixed point results in multiplicative metric spaces, Appl. Math. Nonlinear Sci. 3 (2), 659–668, 2018.
  • [11] R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc. 60, 71–76, 1968.
  • [12] S.G. Matthews, Partial metric topology, Ann. N. Y. Acad. Sci. 728 (1), 183–197, 1994.
  • [13] C. Mongkolkeha and W. Sintunavarat, Best proximity points for multipliative proximal contraction mapping on multiplicative metric spaces, J. Nonlinear Sci. Appl. 8 (6), 1134–1140, 2015.
  • [14] M. Ozavsar and A.C. Cevikel, Fixed points of multiplicative contraction mappings on multiplicative metric spaces, Journal of Engineering Technology and Applied Sciences 2 (2), 65–79, 2017.
  • [15] S. Reich, Some remarks concerning contraction mappings, Can. Math. Bull. 14, 121–124, 1971.
  • [16] A. Robinson, Non-Standard Analysis, Kon. Nederl. Akad. Wetensch. Amsterdam Proc. 23, 432440, 1966.
  • [17] M. Sarwar and Badhah-e-Rome, Some unique fixed point theorems in multiplicative metric space, arXiv:1410.3384v2[math.GM], 2014.
  • [18] D. Stanley, A Multiplicative Calculus, Primus, IX (4), 310–326, 1999.
  • [19] M. Tariq, M. Abbas, A. Hussain, M. Arshad, A. Ali and H. Al-Sulami, Fixed points of non-linear set-valued $(\alpha_*, \varphi_M)$-contraction mappings and related applications, AIMS Math. 7 (5), 8861–8878, 2022.
  • [20] K. Yadav and D. Kumar, Multiplicative $\mathfrak{m}$-metric space, fixed point theorems with applications in multiplicative integrals equation and numerical results, J. Appl. Anal. 30 (1), 173–186, 2024.
  • [21] B. Zada and U. Riaz, Some Fixed Point Results on Multiplicative (b)-metric-like Spaces, Turk. J. Math. 4 (5), 118–131, 2016.

Yıl 2025, Cilt: 54 Sayı: 3, 822 - 833, 24.06.2025

Kapil Yadav , Deepak Kumar

https://doi.org/10.15672/hujms.1336232

Öz

Kaynakça

  • [1] M. Abbas, B. Ali and Y.I. Suleman, Common fixed point of locally contractive mappings in multiplicative metric spaces with application, Int. J. Math. Math. Sci. 2015, 218683, 2015.
  • [2] M. Abbas, M. Da La Sen and T. Nazir, Common fixed point of generalized rational type cocyclic mappings in multiplicative metric space, Discrete Dyn. Nat. Soc. 2015, 532725, 2015.
  • [3] A.A.N. Abdou, Fixed point theorems for generalized contractive mappings in multiplicative metric spaces, J. Nonlinear Sci. Appl. 9 (5), 2347–2363, 2016.
  • [4] M. Asadi, E. Karpinar, and P. Salimi, New extension of p-metric space with some fixed-point results on M-metric spaces, J. Inequal. Appl. 2014, Art. No. 18, 2014.
  • [5] S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fund. Math. 3 (1), 133–181, 1922.
  • [6] A.E. Bashirov, E.M. Kurpinar and A. Ozyapici, Multiplicative calculus and its applications, J. Math. Anal. Appl. 337 (1), 36–48, 2008.
  • [7] S.K. Chatterjea, Fixed point theorems, C.R. Acad. Bulgare Sci. 25, 727–730, 1972.
  • [8] M. Grossman and R. Katz, Non-Newtonian Calculus, Lee Press, Pigeon Cove, MA, 1972.
  • [9] X. He, M. Song and D. Chen, Common fixed points for weak commutative mappings on multiplicative metric space, Fixed Point Theory Appl. 2014, Art. No. 48, 2014 .
  • [10] H. Huang, G. Deng, T. Doenovi and N. Hussain, Note on recent common coupled fixed point results in multiplicative metric spaces, Appl. Math. Nonlinear Sci. 3 (2), 659–668, 2018.
  • [11] R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc. 60, 71–76, 1968.
  • [12] S.G. Matthews, Partial metric topology, Ann. N. Y. Acad. Sci. 728 (1), 183–197, 1994.
  • [13] C. Mongkolkeha and W. Sintunavarat, Best proximity points for multipliative proximal contraction mapping on multiplicative metric spaces, J. Nonlinear Sci. Appl. 8 (6), 1134–1140, 2015.
  • [14] M. Ozavsar and A.C. Cevikel, Fixed points of multiplicative contraction mappings on multiplicative metric spaces, Journal of Engineering Technology and Applied Sciences 2 (2), 65–79, 2017.
  • [15] S. Reich, Some remarks concerning contraction mappings, Can. Math. Bull. 14, 121–124, 1971.
  • [16] A. Robinson, Non-Standard Analysis, Kon. Nederl. Akad. Wetensch. Amsterdam Proc. 23, 432440, 1966.
  • [17] M. Sarwar and Badhah-e-Rome, Some unique fixed point theorems in multiplicative metric space, arXiv:1410.3384v2[math.GM], 2014.
  • [18] D. Stanley, A Multiplicative Calculus, Primus, IX (4), 310–326, 1999.
  • [19] M. Tariq, M. Abbas, A. Hussain, M. Arshad, A. Ali and H. Al-Sulami, Fixed points of non-linear set-valued $(\alpha_*, \varphi_M)$-contraction mappings and related applications, AIMS Math. 7 (5), 8861–8878, 2022.
  • [20] K. Yadav and D. Kumar, Multiplicative $\mathfrak{m}$-metric space, fixed point theorems with applications in multiplicative integrals equation and numerical results, J. Appl. Anal. 30 (1), 173–186, 2024.
  • [21] B. Zada and U. Riaz, Some Fixed Point Results on Multiplicative (b)-metric-like Spaces, Turk. J. Math. 4 (5), 118–131, 2016.
Toplam 21 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Operatör Cebirleri ve Fonksiyonel Analiz
Bölüm Matematik
Yazarlar

Kapil Yadav 0000-0002-9418-9187

Deepak Kumar 0000-0002-1028-5594

Erken Görünüm Tarihi 27 Ağustos 2024
Yayımlanma Tarihi 24 Haziran 2025
Gönderilme Tarihi 22 Mart 2024
Kabul Tarihi 16 Haziran 2024
Yayımlandığı Sayı Yıl 2025 Cilt: 54 Sayı: 3

Kaynak Göster

APA Yadav, K., & Kumar, D. (2025). Common fixed point theorems in multiplicative $\mathfrak{m}$-metric space with applications to the system of multiplicative integral equations and numerical results. Hacettepe Journal of Mathematics and Statistics, 54(3), 822-833. https://doi.org/10.15672/hujms.1336232
AMA Yadav K, Kumar D. Common fixed point theorems in multiplicative $\mathfrak{m}$-metric space with applications to the system of multiplicative integral equations and numerical results. Hacettepe Journal of Mathematics and Statistics. Haziran 2025;54(3):822-833. doi:10.15672/hujms.1336232
Chicago Yadav, Kapil, ve Deepak Kumar. “Common Fixed Point Theorems in Multiplicative $\mathfrak{m}$-Metric Space With Applications to the System of Multiplicative Integral Equations and Numerical Results”. Hacettepe Journal of Mathematics and Statistics 54, sy. 3 (Haziran 2025): 822-33. https://doi.org/10.15672/hujms.1336232.
EndNote Yadav K, Kumar D (01 Haziran 2025) Common fixed point theorems in multiplicative $\mathfrak{m}$-metric space with applications to the system of multiplicative integral equations and numerical results. Hacettepe Journal of Mathematics and Statistics 54 3 822–833.
IEEE K. Yadav ve D. Kumar, “Common fixed point theorems in multiplicative $\mathfrak{m}$-metric space with applications to the system of multiplicative integral equations and numerical results”, Hacettepe Journal of Mathematics and Statistics, c. 54, sy. 3, ss. 822–833, 2025, doi: 10.15672/hujms.1336232.
ISNAD Yadav, Kapil - Kumar, Deepak. “Common Fixed Point Theorems in Multiplicative $\mathfrak{m}$-Metric Space With Applications to the System of Multiplicative Integral Equations and Numerical Results”. Hacettepe Journal of Mathematics and Statistics 54/3 (Haziran 2025), 822-833. https://doi.org/10.15672/hujms.1336232.
JAMA Yadav K, Kumar D. Common fixed point theorems in multiplicative $\mathfrak{m}$-metric space with applications to the system of multiplicative integral equations and numerical results. Hacettepe Journal of Mathematics and Statistics. 2025;54:822–833.
MLA Yadav, Kapil ve Deepak Kumar. “Common Fixed Point Theorems in Multiplicative $\mathfrak{m}$-Metric Space With Applications to the System of Multiplicative Integral Equations and Numerical Results”. Hacettepe Journal of Mathematics and Statistics, c. 54, sy. 3, 2025, ss. 822-33, doi:10.15672/hujms.1336232.
Vancouver Yadav K, Kumar D. Common fixed point theorems in multiplicative $\mathfrak{m}$-metric space with applications to the system of multiplicative integral equations and numerical results. Hacettepe Journal of Mathematics and Statistics. 2025;54(3):822-33.

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