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

Abdurrahman Büyükkaya; Mahpeyker Öztürk

doi:10.33434/cams.1414411

EN

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

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.

Details

Primary Language

English

Subjects

Ordinary Differential Equations, Difference Equations and Dynamical Systems, Pure Mathematics (Other)

Journal Section

Research Article

Authors

Abdurrahman Büyükkaya
0000-0001-6197-8975
Türkiye

Mahpeyker Öztürk ^*
0000-0003-2946-6114
Türkiye

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 Number: 1

DOI

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

IZ

https://izlik.org/JA99JS79HH

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

1.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. doi:10.33434/cams.1414411

Chicago

Büyükkaya, Abdurrahman, and Mahpeyker Öztürk. 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.

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

[1]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, Mar. 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 1, 2024): 27-41. https://doi.org/10.33434/cams.1414411.

JAMA

1.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, Mar. 2024, pp. 27-41, doi:10.33434/cams.1414411.

Vancouver

1.Abdurrahman Büyükkaya, Mahpeyker Öztürk. On Suzuki-Proinov Type Contractions in Modular $b$-Metric Spaces with an Application. Communications in Advanced Mathematical Sciences. 2024 Mar. 1;7(1):27-41. doi:10.33434/cams.1414411

The published articles in CAMS are licensed under a Creative Commons Attribution-NonCommercial 4.0 International License..

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

Abstract

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

Abstract

Keywords

References

Details

Primary Language

Subjects

Journal Section

Authors

Early Pub Date

Publication Date

Submission Date

Acceptance Date

Published in Issue

DOI

IZ

Cite

Cited By

On Modular b-Metrics

Some convergence results in modular spaces with application to a system of integral equations

Enhancing Generalized Interpolative Contraction Through Simulation Functions

Solutions of Equilibrium Problems with Fixed Point Iteration Method and Data Dependence