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On Suzuki-Proinov Type Contractions in Modular $b$-Metric Spaces with an Application

Year 2024, Volume: 7 Issue: 1, 27 - 41, 04.03.2024

Abdurrahman Büyükkaya Mahpeyker Öztürk

https://doi.org/10.33434/cams.1414411

Abstract

In this paper, by taking ${{\mathcal C}_\mathcal{A}}-$simulation function and Proinov type function into account, we set up a new contraction mapping called Suzuki$-$Proinov $\mathpzc{Z^*}_{\aE^*}^{\aR}(\alpha)-$contraction, including both rational expressions that possess quadratic terms and $\aE-$type contractions. Furthermore, we demonstrate a common fixed point theorem through the mappings endowed with triangular $\alpha-$admissibility in the setting of modular $b-$metric spaces. Besides that, we achieve some new outcomes that contribute to the current ones in the literature through the main theorem, and, as an application, we examine the existence of solutions to a class of functional equations emerging in dynamic programming.

Keywords

Common fixed point Dynamic programming Modular $b-$metric space Proinov type mappings Simulation functions

References

  • [1] S. Banach, Sur les operations dans les emsembles abstraits et leurs applications aux equations integrales, Fund. Math., 1 (1922) 133-181.
  • [2] M. Younis, A. A. N. Abdou, Novel fuzzy contractions and applications to engineering science, Fractal Fract., 8 (2024), 28.
  • [3] M. Younis, D. Singh, A. A. N. Abdou, A fixed point approach for tuning circuit problem in b-dislocated metric spaces, Math. Methods Appl. Sci., 45 (2022), 2234–2253.
  • [4] M. Younis, D. Bahuguna, A unique approach to graph-based metric spaces with an application to rocket ascension, Comput. Appl. Math., 42 (2023), 44.
  • [5] 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.
  • [6] I. A. Bakhtin, The contraction mapping principle in quasimetric spaces, Funct. Anal. Unianowsk Gos. Ped. Inst., 30 (1989) 26–37.
  • [7] S. Czerwik, Contraction mappings in b􀀀metric spaces, Acta. Math. Inform. Univ. Ostrav., 1(1) (1993), 5-11.
  • [8] S. Czerwik, Nonlinear set-valued contraction mappings in b􀀀metric spaces, Atti Semin. Mat. Fis. Univ.Modena, 46 (1998), 263-276.
  • [9] A. Aghajani, M. Abbas, J. R. Roshan, Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces, Math. Slovaca, 64(4) (2014), 941–960.
  • [10] V. V. Chistyakov,Modular metric spaces, I: Basic concepts, Nonlinear Anal., 72 (2010), 1-14.
  • [11] V. V. Chistyakov, Modular metric spaces, II: Application to superposition operators, Nonlinear Anal., 72 (2010), 15-30.
  • [12] M. E. Ege, C. Alaca, Some results for modular b􀀀metric spaces and an application to a system of linear equations, Azerbaijan J. Math. 8(1) (2018), 3-14.
  • [13] V. Parvaneh, N. Hussain, M. Khorshidi, N. Mlaiki, H. Aydi, Fixed point results for generalized F􀀀contractions in modular b-metric spaces with applications, Mathematics, 7(10) (2019), 1-16.
  • [14] M. Öztürk, A. Bu¨yu¨kkaya, Fixed point results for Suzuki-type S􀀀contractions via simulation functions in modular b-metric spaces, Math Meth Appl Sci., 45 (2022), 12167-12183. https://doi.org/10.1002/mma.7634
  • [15] A. Büyükkaya, M. Öztürk, Some fixed point results for Sehgal-Proinov type contractions in modular b-metric spaces, Analele Stiint. Ale Univ. Ovidius Constanta Ser. Mat., 31(3) (2023), 61-85.
  • [16] A. Büyükkaya, A. Fulga, M. Öztürk, On Generalized Suzuki-Proinov type $\left( {\alpha,{\mathcal{Z}}_E ^*} \right) - $contractions in modular $b-$metric spaces, Filomat, 37(4) (2023), 1207–1222.
  • [17] M. Öztürk, F. Golkarmanesh, A. Büyükkaya, V. Parvaneh, Generalized almost simulative ${\hat Z}_{_{\Psi ^*} }^\Theta - $contraction mappings in modular b􀀀metric spaces, J. Math. Ext., 17(2) (2023), 1-37.
  • [18] F. Khojasteh, S. Shukla, S. Radenovic, A new approach to the study of fixed point theorems for simulation functions, Filomat, 29 (2015), 1189-1194.
  • [19] A. Fulga, A. M. Proca, Fixed point for Geraghty JE􀀀contractions, J. Nonlinear Sci. Appl., 10 (2017), 5125-5131.
  • [20] A. Fulga, A. M. Proca, A new Generalization of Wardowski fixed point theorem in complete metric spaces, Adv. Theory Nonlinear Anal. Appl., 1 (2017), 57-63.
  • [21] A. Fulga, E. Karapınar, Some results on S􀀀contractions of Type E, Mathematics, 195 (6) (2018), 1-9.
  • [22] B. Alqahtani, A. Fulga, E. Karapınar, A short note on the common fixed points of the Geraghty contraction of type ${E_{S, T}}$}, Demonstr. Math., 51 (2018), 233-240.
  • [23] A. Fulga, E. Karapınar, Some results on S􀀀contractions of Type E, Mathematics, 195(6) (2018), 1-9.
  • [24] A. H. Ansari, Note on ”$\varphi - \psi - $contractive type mappings and related fixed point”, In The 2qd Regional Conference on Mathematics and Applications, Payame Noor University, (2014), 377-380.
  • [25] S. Radenovic, S. Chandok, Simulation type functions and coincidence point results, Filomat, 32 (2018), 141–147.
  • [26] T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 (2009), 5313–5317.
  • [27] P. Proinov, Fixed point theorems for generalized contractive mappings in metric spaces, J. Fixed Point Theory Appl., 22 (2020), 21.
  • [28] E. Karapınar, A. Fulga, A Fixed point theorem for Proinov mappings with a contractive iterate, Appl. Math. J. Chinese Univ. 38 (2023), 403–412.
  • [29] E. Karapınar, A. Fulga, Discussions on Proinov􀀀Cb􀀀contraction mapping on b􀀀metric space, J. Funct. Spaces, ID:1411808 (2023). https://doi.org/10.1155/2023/1411808
  • [30] E. Karapınar, M. De La Sen, A. Fulga, A note on the Gornicki-Proinov type contraction, J. Funct. Spaces 2021 (2021). https://doi.org/10.1155/2021/6686644
  • [31] E. Karapınar, A. Fulga, S.S. Yesilkaya, Fixed points of Proinov type multivalued mappings on quasi metric spaces, J. Funct. Spaces, ID:7197541 (2022). https://doi.org/10.1155/2022/7197541
  • [32] E. Karapınar, J. Martinez-Moreno, N. Shahzad, A.F. Roldan Lopez de Hierro, Extended Proinov X􀀀contractions in metric spaces and fuzzy metric spaces satisfying the property N C by avoiding the monotone condition, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat., 116(4) (2022), 1-28.
  • [33] A. F. Roldan Lopez de Hierro, A. Fulga, E. Karapınar, N. Shahzad, Proinov type fixed point results in non-Archimedean fuzzy metric spaces, Mathematics, 9(14) (2021), 1594.
  • [34] M. Zhou, X. Liu, N. Saleem, A. Fulga, N. Özzür, A new study on the fixed point sets of Proinov-type contractions via rational forms, Symmetry, 14(1) (2022), 93.
  • [35] M. Zhou, N. Saleem, X. Liu, A. Fulga, A. F. Rold´an Lopez de Hierro, A new approach to Proinov-type fixed point results in Non-archimedean fuzzy metric spaces, Mathematics, 9(23) (2021), 3001.
  • [36] B. Samet, C. Vetro, P. Vetro, Fixed point theorems for a􀀀y􀀀contractive mappings, Nonlinear Anal., 75 (2012), 2154-2165
  • [37] O. Popescu, Some new fixed point theorems for a􀀀Geraghty contraction type maps in metric spaces, Fixed Point Theory Appl., 2014 (2014), 190.
  • [38] E. Karapınar, P. Kumam, P. Salimi, On $\alpha - \mathpzc{Q}-$Meir-Keeler contractive mappings, Fixed Point Theory Appl., 2013 (2013), 1-12.
  • [39] H. Qawaqneh, M. S. M. Noorani, W. Shatanawi, H. Alsamir, Common fixed points for pairs of triangular a􀀀admissible mappings, J. Nonlinear Sci. Appl., 10 (2017), 6192–6204.

Year 2024, Volume: 7 Issue: 1, 27 - 41, 04.03.2024

Abdurrahman Büyükkaya Mahpeyker Öztürk

https://doi.org/10.33434/cams.1414411

Abstract

References

  • [1] S. Banach, Sur les operations dans les emsembles abstraits et leurs applications aux equations integrales, Fund. Math., 1 (1922) 133-181.
  • [2] M. Younis, A. A. N. Abdou, Novel fuzzy contractions and applications to engineering science, Fractal Fract., 8 (2024), 28.
  • [3] M. Younis, D. Singh, A. A. N. Abdou, A fixed point approach for tuning circuit problem in b-dislocated metric spaces, Math. Methods Appl. Sci., 45 (2022), 2234–2253.
  • [4] M. Younis, D. Bahuguna, A unique approach to graph-based metric spaces with an application to rocket ascension, Comput. Appl. Math., 42 (2023), 44.
  • [5] 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.
  • [6] I. A. Bakhtin, The contraction mapping principle in quasimetric spaces, Funct. Anal. Unianowsk Gos. Ped. Inst., 30 (1989) 26–37.
  • [7] S. Czerwik, Contraction mappings in b􀀀metric spaces, Acta. Math. Inform. Univ. Ostrav., 1(1) (1993), 5-11.
  • [8] S. Czerwik, Nonlinear set-valued contraction mappings in b􀀀metric spaces, Atti Semin. Mat. Fis. Univ.Modena, 46 (1998), 263-276.
  • [9] A. Aghajani, M. Abbas, J. R. Roshan, Common fixed point of generalized weak contractive mappings in partially ordered b-metric spaces, Math. Slovaca, 64(4) (2014), 941–960.
  • [10] V. V. Chistyakov,Modular metric spaces, I: Basic concepts, Nonlinear Anal., 72 (2010), 1-14.
  • [11] V. V. Chistyakov, Modular metric spaces, II: Application to superposition operators, Nonlinear Anal., 72 (2010), 15-30.
  • [12] M. E. Ege, C. Alaca, Some results for modular b􀀀metric spaces and an application to a system of linear equations, Azerbaijan J. Math. 8(1) (2018), 3-14.
  • [13] V. Parvaneh, N. Hussain, M. Khorshidi, N. Mlaiki, H. Aydi, Fixed point results for generalized F􀀀contractions in modular b-metric spaces with applications, Mathematics, 7(10) (2019), 1-16.
  • [14] M. Öztürk, A. Bu¨yu¨kkaya, Fixed point results for Suzuki-type S􀀀contractions via simulation functions in modular b-metric spaces, Math Meth Appl Sci., 45 (2022), 12167-12183. https://doi.org/10.1002/mma.7634
  • [15] A. Büyükkaya, M. Öztürk, Some fixed point results for Sehgal-Proinov type contractions in modular b-metric spaces, Analele Stiint. Ale Univ. Ovidius Constanta Ser. Mat., 31(3) (2023), 61-85.
  • [16] A. Büyükkaya, A. Fulga, M. Öztürk, On Generalized Suzuki-Proinov type $\left( {\alpha,{\mathcal{Z}}_E ^*} \right) - $contractions in modular $b-$metric spaces, Filomat, 37(4) (2023), 1207–1222.
  • [17] M. Öztürk, F. Golkarmanesh, A. Büyükkaya, V. Parvaneh, Generalized almost simulative ${\hat Z}_{_{\Psi ^*} }^\Theta - $contraction mappings in modular b􀀀metric spaces, J. Math. Ext., 17(2) (2023), 1-37.
  • [18] F. Khojasteh, S. Shukla, S. Radenovic, A new approach to the study of fixed point theorems for simulation functions, Filomat, 29 (2015), 1189-1194.
  • [19] A. Fulga, A. M. Proca, Fixed point for Geraghty JE􀀀contractions, J. Nonlinear Sci. Appl., 10 (2017), 5125-5131.
  • [20] A. Fulga, A. M. Proca, A new Generalization of Wardowski fixed point theorem in complete metric spaces, Adv. Theory Nonlinear Anal. Appl., 1 (2017), 57-63.
  • [21] A. Fulga, E. Karapınar, Some results on S􀀀contractions of Type E, Mathematics, 195 (6) (2018), 1-9.
  • [22] B. Alqahtani, A. Fulga, E. Karapınar, A short note on the common fixed points of the Geraghty contraction of type ${E_{S, T}}$}, Demonstr. Math., 51 (2018), 233-240.
  • [23] A. Fulga, E. Karapınar, Some results on S􀀀contractions of Type E, Mathematics, 195(6) (2018), 1-9.
  • [24] A. H. Ansari, Note on ”$\varphi - \psi - $contractive type mappings and related fixed point”, In The 2qd Regional Conference on Mathematics and Applications, Payame Noor University, (2014), 377-380.
  • [25] S. Radenovic, S. Chandok, Simulation type functions and coincidence point results, Filomat, 32 (2018), 141–147.
  • [26] T. Suzuki, A new type of fixed point theorem in metric spaces, Nonlinear Anal., 71 (2009), 5313–5317.
  • [27] P. Proinov, Fixed point theorems for generalized contractive mappings in metric spaces, J. Fixed Point Theory Appl., 22 (2020), 21.
  • [28] E. Karapınar, A. Fulga, A Fixed point theorem for Proinov mappings with a contractive iterate, Appl. Math. J. Chinese Univ. 38 (2023), 403–412.
  • [29] E. Karapınar, A. Fulga, Discussions on Proinov􀀀Cb􀀀contraction mapping on b􀀀metric space, J. Funct. Spaces, ID:1411808 (2023). https://doi.org/10.1155/2023/1411808
  • [30] E. Karapınar, M. De La Sen, A. Fulga, A note on the Gornicki-Proinov type contraction, J. Funct. Spaces 2021 (2021). https://doi.org/10.1155/2021/6686644
  • [31] E. Karapınar, A. Fulga, S.S. Yesilkaya, Fixed points of Proinov type multivalued mappings on quasi metric spaces, J. Funct. Spaces, ID:7197541 (2022). https://doi.org/10.1155/2022/7197541
  • [32] E. Karapınar, J. Martinez-Moreno, N. Shahzad, A.F. Roldan Lopez de Hierro, Extended Proinov X􀀀contractions in metric spaces and fuzzy metric spaces satisfying the property N C by avoiding the monotone condition, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat., 116(4) (2022), 1-28.
  • [33] A. F. Roldan Lopez de Hierro, A. Fulga, E. Karapınar, N. Shahzad, Proinov type fixed point results in non-Archimedean fuzzy metric spaces, Mathematics, 9(14) (2021), 1594.
  • [34] M. Zhou, X. Liu, N. Saleem, A. Fulga, N. Özzür, A new study on the fixed point sets of Proinov-type contractions via rational forms, Symmetry, 14(1) (2022), 93.
  • [35] M. Zhou, N. Saleem, X. Liu, A. Fulga, A. F. Rold´an Lopez de Hierro, A new approach to Proinov-type fixed point results in Non-archimedean fuzzy metric spaces, Mathematics, 9(23) (2021), 3001.
  • [36] B. Samet, C. Vetro, P. Vetro, Fixed point theorems for a􀀀y􀀀contractive mappings, Nonlinear Anal., 75 (2012), 2154-2165
  • [37] O. Popescu, Some new fixed point theorems for a􀀀Geraghty contraction type maps in metric spaces, Fixed Point Theory Appl., 2014 (2014), 190.
  • [38] E. Karapınar, P. Kumam, P. Salimi, On $\alpha - \mathpzc{Q}-$Meir-Keeler contractive mappings, Fixed Point Theory Appl., 2013 (2013), 1-12.
  • [39] H. Qawaqneh, M. S. M. Noorani, W. Shatanawi, H. Alsamir, Common fixed points for pairs of triangular a􀀀admissible mappings, J. Nonlinear Sci. Appl., 10 (2017), 6192–6204.
There are 39 citations in total.

Details

Primary Language English
Subjects Ordinary Differential Equations, Difference Equations and Dynamical Systems, Pure Mathematics (Other)
Journal Section Articles
Authors

Abdurrahman Büyükkaya 0000-0001-6197-8975

Mahpeyker Öztürk 0000-0003-2946-6114

Early Pub Date February 19, 2024
Publication Date March 4, 2024
Submission Date January 3, 2024
Acceptance Date February 13, 2024
Published in Issue Year 2024 Volume: 7 Issue: 1

Cite

APA Büyükkaya, A., & Öztürk, M. (2024). On Suzuki-Proinov Type Contractions in Modular $b$-Metric Spaces with an Application. Communications in Advanced Mathematical Sciences, 7(1), 27-41. https://doi.org/10.33434/cams.1414411
AMA Büyükkaya A, Öztürk M. On Suzuki-Proinov Type Contractions in Modular $b$-Metric Spaces with an Application. Communications in Advanced Mathematical Sciences. March 2024;7(1):27-41. doi:10.33434/cams.1414411
Chicago Büyükkaya, Abdurrahman, and Mahpeyker Öztürk. “On Suzuki-Proinov Type Contractions in Modular $b$-Metric Spaces With an Application”. Communications in Advanced Mathematical Sciences 7, no. 1 (March 2024): 27-41. https://doi.org/10.33434/cams.1414411.
EndNote Büyükkaya A, Öztürk M (March 1, 2024) On Suzuki-Proinov Type Contractions in Modular $b$-Metric Spaces with an Application. Communications in Advanced Mathematical Sciences 7 1 27–41.
IEEE A. Büyükkaya and M. Öztürk, “On Suzuki-Proinov Type Contractions in Modular $b$-Metric Spaces with an Application”, Communications in Advanced Mathematical Sciences, vol. 7, no. 1, pp. 27–41, 2024, doi: 10.33434/cams.1414411.
ISNAD Büyükkaya, Abdurrahman - Öztürk, Mahpeyker. “On Suzuki-Proinov Type Contractions in Modular $b$-Metric Spaces With an Application”. Communications in Advanced Mathematical Sciences 7/1 (March 2024), 27-41. https://doi.org/10.33434/cams.1414411.
JAMA Büyükkaya A, Öztürk M. On Suzuki-Proinov Type Contractions in Modular $b$-Metric Spaces with an Application. Communications in Advanced Mathematical Sciences. 2024;7:27–41.
MLA Büyükkaya, Abdurrahman and Mahpeyker Öztürk. “On Suzuki-Proinov Type Contractions in Modular $b$-Metric Spaces With an Application”. Communications in Advanced Mathematical Sciences, vol. 7, no. 1, 2024, pp. 27-41, doi:10.33434/cams.1414411.
Vancouver Büyükkaya A, Öztürk M. On Suzuki-Proinov Type Contractions in Modular $b$-Metric Spaces with an Application. Communications in Advanced Mathematical Sciences. 2024;7(1):27-41.
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