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Yıl 2025, Cilt: 8 Sayı: 1, 8 - 20, 25.03.2025

Mudasir Younis , Mahpeyker Öztürk

https://doi.org/10.32323/ujma.1597874
Cited By: 1

Öz

Kaynakça

  • [1] M. M. Frechet, Sur quelques points du calcul fonctionnel, Rend. Circ. Mat. Palermo, 22(1) (1906), 1-72.
  • [2] T. Kamran, M. Samreen, Q. Ul. Ain, A generalization of b-metric space and some fixed point theorems, Math., 5(2) (2017), 1-19.
  • [3] S. Basha, P. Veeramani, Best approximations and best proximity pairs, Acta Sci. Math, 63 (1997), 289-300.
  • [4] S. Basha and P. Veeramani, Best proximity pair theorems for multifunction with open fibers, J. Approx. Theory, 103(1) (2000), 119-129.
  • [5] S. Ghezellou, M. Azhini, M. Asadi, Best proximity point theorems by K, C and MT types in b-metric spaces with an application. Int. J. Nonlinear Anal. Appl., 12(2) (2021), 1317-1329.
  • [6] T. Suzuki, M. Kikkawa, C. Vetro, The existence of best proximity points in metric spaces with the property UC, Nonlinear Anal., 71(7-8) (2009), 2918-2926.
  • [7] M. Asadi, M. Afshar, Fixed point theorems in the generalized rational type of C-class functions in b-metric spaces with application to integral equation. 3c Empresa: Investigaci´on y pensamiento crtico, 11(2) (2022), 64-74.
  • [8] B. Alqahtani, A. Fulg, E. Karapınar, Common fixed point results on an extended b-metric space, J. Inequal. Appl., 2018(1) (2018), 1-15.
  • [9] S. Chandok, E. Karapinar, Common fixed point of generalized rational type contraction mappings in partially ordered metric spaces, Thai J. Math., 11(2) (2012), 251-260.
  • [10] S. Jabeen, S. Ur Rehman, Z. Zheng, W. Wei, Weakly compatible and quasi-contraction results in fuzzy cone metric spaces with application to the Urysohn type integral equations, Adv. Differ. Equ., 2020, 280. https://doi.org/10.1186/s13662-020-02743-5
  • [11] R. McConnell, R. Kwok, J. Curlander, W. Kober, S. Pang, Y-S correlation and dynamic time warping: Two methods for tracking ice floes, IEEE Trans. Geosci. Remote Sens., 29 (1991), 1004–1012.
  • [12] M. Younis, D. Singh, I. Altun, V. Chauhan, Graphical structure of extended b-metric spaces: An application to the transverse oscillations of a homogeneous bar, Internat. J. Nonlinear Sci. Numer. Simul., 23(7-8) (2022), 1239-1252. https://doi.org/10.1515/ijnsns-2020-0126
  • [13] M. Younis, H. Ahmad, L. Chen, M. Han, Computation and convergence of fixed points in graphical spaces with an application to elastic beam deformations, J. Geom. Phys., 192 (2023), 104955. https://doi.org/10.1016/j.geomphys.2023.104955.
  • [14] M. Younis, D. Singh, M. Asadi, V. Joshi, Results on contractions of Reich type in graphical b-metric spaces with applications, Filomat, 33(17) (2019), 5723-5735.
  • [15] M. E. Samani, S. M. Vaezpour, M. Asadi, New fixed point results with aqsp -admissible contractions on b-Branciari metric spaces, J. Inequal. Spec. Funct., 9(4) (2018), 101-112.
  • [16] N. Savanovic, I. D. Arandelovic, Z. D. Mitrovic, The results on coincidence and common fixed points for a new type multi-valued mappings in b-metric spaces, Math., 10(6) (2022), 856.
  • [17] M. Younis, H. Ahmad, W. Shahid, Best proximity points for multi-valued mappings and equation of motion, J. Appl. Anal. Comput., 14(1) (2024), 298-316.
  • [18] V. S. Raj, A best proximity point theorem for weakly contractive non-self-mappings, Nonlinear. Anal., 74(2011), 4804–4808.
  • [19] T. R. Rockafellar, R. J. V. Wets, Variational Analysis, Springer Berlin, Germany, (2005).
  • [20] M. Gabeleh, C. Vetro, A note on best proximity point theory using proximal-contractions, J. Fixed Point Theory Appl., 20(4) (2018), 1-11.
  • [21] N. Saleem, J. Vujakovi´c, W.U. Baloch, S. Radenovic, Coincidence point results for multi-valued Suzuki type mappings using q-contraction in b-metric spaces, Math., 7(11) (2019), 1017.
  • [22] M.S. Khan, M. Ozair, T. Hussain, J. F. Gomez-Aguilar, Bifurcation analysis of a discrete-time compartmental model for hypertensive or diabetic patients exposed to COVID-19, The European Physical Journal Plus, 136(8), (2021), 1-26.
  • [23] A. A. N. Abdou, Solving a nonlinear fractional differential equation using fixed point results in orthogonal metric spaces, Fractal Fract., 7(11) (2023), 817. https://doi.org/10.3390/fractalfract7110817
  • [24] N. I. Hamdan, S. A., Kechil, Mathematical model of COVID-19 transmission using the fractional-order differential equation. In AIP Conference Proceedings, AIP Publishing, 2905(1) (2024).
  • [25] A. Cabada, Z. Hamdi, Nonlinear fractional differential equations with integral boundary value conditions, Appl. Math. Comput., 228(1) (2014), 251-257.

Some Novel Proximal Point Results and Applications

Yıl 2025, Cilt: 8 Sayı: 1, 8 - 20, 25.03.2025

Mudasir Younis , Mahpeyker Öztürk

https://doi.org/10.32323/ujma.1597874
Cited By: 1

Öz

The current study provides significant findings on coincidence the best proximity points for proximal-contractions in the context of extended $b$-metric spaces. To substantiate our assertions, we present illustrative examples across several circumstances. The conclusions presented in this study provide an expanded and more nuanced viewpoint, extending and generalizing multiple previous findings in optimal proximity theory. These findings present a new method for comprehending proximal coincidence locations in multi-valued mappings, representing a substantial advancement in the existing research landscape. This work gives practical benchmarks for implementing optimal proximity results, provided that existence and uniqueness constraints are met.

Anahtar Kelimeler

Best proximity point Boundary value problem Coincidence point Extended $b$--metric

Kaynakça

  • [1] M. M. Frechet, Sur quelques points du calcul fonctionnel, Rend. Circ. Mat. Palermo, 22(1) (1906), 1-72.
  • [2] T. Kamran, M. Samreen, Q. Ul. Ain, A generalization of b-metric space and some fixed point theorems, Math., 5(2) (2017), 1-19.
  • [3] S. Basha, P. Veeramani, Best approximations and best proximity pairs, Acta Sci. Math, 63 (1997), 289-300.
  • [4] S. Basha and P. Veeramani, Best proximity pair theorems for multifunction with open fibers, J. Approx. Theory, 103(1) (2000), 119-129.
  • [5] S. Ghezellou, M. Azhini, M. Asadi, Best proximity point theorems by K, C and MT types in b-metric spaces with an application. Int. J. Nonlinear Anal. Appl., 12(2) (2021), 1317-1329.
  • [6] T. Suzuki, M. Kikkawa, C. Vetro, The existence of best proximity points in metric spaces with the property UC, Nonlinear Anal., 71(7-8) (2009), 2918-2926.
  • [7] M. Asadi, M. Afshar, Fixed point theorems in the generalized rational type of C-class functions in b-metric spaces with application to integral equation. 3c Empresa: Investigaci´on y pensamiento crtico, 11(2) (2022), 64-74.
  • [8] B. Alqahtani, A. Fulg, E. Karapınar, Common fixed point results on an extended b-metric space, J. Inequal. Appl., 2018(1) (2018), 1-15.
  • [9] S. Chandok, E. Karapinar, Common fixed point of generalized rational type contraction mappings in partially ordered metric spaces, Thai J. Math., 11(2) (2012), 251-260.
  • [10] S. Jabeen, S. Ur Rehman, Z. Zheng, W. Wei, Weakly compatible and quasi-contraction results in fuzzy cone metric spaces with application to the Urysohn type integral equations, Adv. Differ. Equ., 2020, 280. https://doi.org/10.1186/s13662-020-02743-5
  • [11] R. McConnell, R. Kwok, J. Curlander, W. Kober, S. Pang, Y-S correlation and dynamic time warping: Two methods for tracking ice floes, IEEE Trans. Geosci. Remote Sens., 29 (1991), 1004–1012.
  • [12] M. Younis, D. Singh, I. Altun, V. Chauhan, Graphical structure of extended b-metric spaces: An application to the transverse oscillations of a homogeneous bar, Internat. J. Nonlinear Sci. Numer. Simul., 23(7-8) (2022), 1239-1252. https://doi.org/10.1515/ijnsns-2020-0126
  • [13] M. Younis, H. Ahmad, L. Chen, M. Han, Computation and convergence of fixed points in graphical spaces with an application to elastic beam deformations, J. Geom. Phys., 192 (2023), 104955. https://doi.org/10.1016/j.geomphys.2023.104955.
  • [14] M. Younis, D. Singh, M. Asadi, V. Joshi, Results on contractions of Reich type in graphical b-metric spaces with applications, Filomat, 33(17) (2019), 5723-5735.
  • [15] M. E. Samani, S. M. Vaezpour, M. Asadi, New fixed point results with aqsp -admissible contractions on b-Branciari metric spaces, J. Inequal. Spec. Funct., 9(4) (2018), 101-112.
  • [16] N. Savanovic, I. D. Arandelovic, Z. D. Mitrovic, The results on coincidence and common fixed points for a new type multi-valued mappings in b-metric spaces, Math., 10(6) (2022), 856.
  • [17] M. Younis, H. Ahmad, W. Shahid, Best proximity points for multi-valued mappings and equation of motion, J. Appl. Anal. Comput., 14(1) (2024), 298-316.
  • [18] V. S. Raj, A best proximity point theorem for weakly contractive non-self-mappings, Nonlinear. Anal., 74(2011), 4804–4808.
  • [19] T. R. Rockafellar, R. J. V. Wets, Variational Analysis, Springer Berlin, Germany, (2005).
  • [20] M. Gabeleh, C. Vetro, A note on best proximity point theory using proximal-contractions, J. Fixed Point Theory Appl., 20(4) (2018), 1-11.
  • [21] N. Saleem, J. Vujakovi´c, W.U. Baloch, S. Radenovic, Coincidence point results for multi-valued Suzuki type mappings using q-contraction in b-metric spaces, Math., 7(11) (2019), 1017.
  • [22] M.S. Khan, M. Ozair, T. Hussain, J. F. Gomez-Aguilar, Bifurcation analysis of a discrete-time compartmental model for hypertensive or diabetic patients exposed to COVID-19, The European Physical Journal Plus, 136(8), (2021), 1-26.
  • [23] A. A. N. Abdou, Solving a nonlinear fractional differential equation using fixed point results in orthogonal metric spaces, Fractal Fract., 7(11) (2023), 817. https://doi.org/10.3390/fractalfract7110817
  • [24] N. I. Hamdan, S. A., Kechil, Mathematical model of COVID-19 transmission using the fractional-order differential equation. In AIP Conference Proceedings, AIP Publishing, 2905(1) (2024).
  • [25] A. Cabada, Z. Hamdi, Nonlinear fractional differential equations with integral boundary value conditions, Appl. Math. Comput., 228(1) (2014), 251-257.
Toplam 25 adet kaynakça vardır.

Ayrıntılar

Birincil Dil İngilizce
Konular Temel Matematik (Diğer)
Bölüm Makaleler
Yazarlar

Mudasir Younis 0000-0001-5499-4272

Mahpeyker Öztürk 0000-0003-2946-6114

Erken Görünüm Tarihi 23 Şubat 2025
Yayımlanma Tarihi 25 Mart 2025
Gönderilme Tarihi 7 Aralık 2024
Kabul Tarihi 22 Şubat 2025
Yayımlandığı Sayı Yıl 2025 Cilt: 8 Sayı: 1

Kaynak Göster

APA Younis, M., & Öztürk, M. (2025). Some Novel Proximal Point Results and Applications. Universal Journal of Mathematics and Applications, 8(1), 8-20. https://doi.org/10.32323/ujma.1597874
AMA Younis M, Öztürk M. Some Novel Proximal Point Results and Applications. Univ. J. Math. Appl. Mart 2025;8(1):8-20. doi:10.32323/ujma.1597874
Chicago Younis, Mudasir, ve Mahpeyker Öztürk. “Some Novel Proximal Point Results and Applications”. Universal Journal of Mathematics and Applications 8, sy. 1 (Mart 2025): 8-20. https://doi.org/10.32323/ujma.1597874.
EndNote Younis M, Öztürk M (01 Mart 2025) Some Novel Proximal Point Results and Applications. Universal Journal of Mathematics and Applications 8 1 8–20.
IEEE M. Younis ve M. Öztürk, “Some Novel Proximal Point Results and Applications”, Univ. J. Math. Appl., c. 8, sy. 1, ss. 8–20, 2025, doi: 10.32323/ujma.1597874.
ISNAD Younis, Mudasir - Öztürk, Mahpeyker. “Some Novel Proximal Point Results and Applications”. Universal Journal of Mathematics and Applications 8/1 (Mart 2025), 8-20. https://doi.org/10.32323/ujma.1597874.
JAMA Younis M, Öztürk M. Some Novel Proximal Point Results and Applications. Univ. J. Math. Appl. 2025;8:8–20.
MLA Younis, Mudasir ve Mahpeyker Öztürk. “Some Novel Proximal Point Results and Applications”. Universal Journal of Mathematics and Applications, c. 8, sy. 1, 2025, ss. 8-20, doi:10.32323/ujma.1597874.
Vancouver Younis M, Öztürk M. Some Novel Proximal Point Results and Applications. Univ. J. Math. Appl. 2025;8(1):8-20.

Cited By

Mutually nearest solution of a system of differential and integro-differential equations via proximal Branciari condensing operators
Research in Mathematics
https://doi.org/10.1080/27684830.2025.2500824
 Kapak Resmi İndir

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Universal Journal of Mathematics and Applications 

29207               

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