$(\psi, \mathcal{GF})$-CONTRACTION MAPPINGS AND RELATED FIXED POINT RESULTS IN PARTIAL MODULAR METRIC SPACES

Santanu Narzary; Liza Hazarika; Dipankar Das

$(\psi, \mathcal{GF})$-CONTRACTION MAPPINGS AND RELATED FIXED POINT RESULTS IN PARTIAL MODULAR METRIC SPACES

Abstract

In this paper, we focus on establishing the existence of fixed points results for $ (\psi, \mathcal{GF}) $-contraction mapping in partial modular metric spaces. In support of this result, a suitable example is given. For the application, we demonstrate how these results can be utilized to investigate the existence and uniqueness of solutions for a system of $\mathcal{V}$olterra-type integral equation. Moreover, we demonstrate the existence of solutions of fractional differential equations in the framework of partial modular metric spaces.

Keywords

References

[1] Bai, Z. and Lü, H., (2005), Positive solutions for boundary value problem of nonlinear fractional differential equation, Journal of mathematical analysis and applications, 311(2), p.9502748, pp.495- 505.
[2] Baleanu, D., Rezapour, S. and Mohammadi, H., (2013), Some existence results on nonlinear fractional differential equations, Philosophical Transactions of the Royal Society A: Mathematical, Physical and Engineering Sciences, 371(1990), p.20120144, pp.1-5.
[3] Bonab, S. H., Parvaneh, V., Bagheri, Z. and Shahkoohi, R. J., (2023), Extended Interpolative Hardy–Rogers–Geraghty–Wardowski Contractions and an Application, Advances in Number Theory and Applied Analysis, pp.261-277.
[4] Chandok, S., Kumar, D. and Park, C., (2019), C∗-algebra-valued partial metric space and fixed point theorems, Proceedings-Mathematical Sciences, 129(3), p.0037, pp.1-9.
[5] Chandok, S., Sharma, R. K. and Radenovi´c, S., (2021), Multivalued problems via orthogonal contraction mappings with application to fractional differential equation, Journal of Fixed Point Theory and Applications, 23(2), p.14, pp.1-14.
[6] Chistyakov, V. V., (2010), Modular metric spaces, I: basic concepts, Nonlinear Analysis: Theory, Methods & Applications, 72(1), pp.1-14.
[7] Das, D., Narzary, S. and Bora, N., (2022), Some Fixed Point Results in Modular-like Metric Spaces and Partial Modular-like Metric Spaces with Its Non-Archimedean Version, Advances and Application in Mathematical Sciences, 21(10), pp.5997-6016.
[8] Das, D., Narzary, S., Singh, Y. M., Khan, M. S. and Sessa, S., (2022), Fixed point results on partial modular metric space, Axioms, 11(2), p.62, pp.1-18.

[9] Guran, L., Mitrovic, Z. D., Reddy, G. S. M., Belhenniche, A. and Radenovi´c, S., (2021), Applications of a fixed point result for solving nonlinear fractional and integral differential equations, Fractal and Fractional, 5(4), p.211, pp.1-13.
[10] Hosseinzadeh, H. and Parvaneh, V., (2020), Meir–Keeler type contractive mappings in modular and partial modular metric spaces, Asian-European Journal of Mathematics, 13(05), p.2050087, pp.1-18.
[11] Khamsi, M. A., (1996), A convexity property in modular function spaces, Mathematica Japonica, 44(2), pp.269-280.
[12] Kozlowski, W. M., (1988), Notes on modular function spaces, II. Commentationes Mathematicae, 28(1), pp.87-100.
[13] Massit, H. and Rossafi, M., (2021), Fixed Point Theorem for (ϕ, F)- contraction on C∗-algebra valued metric spaces, European Journal of Mathematics and Applications, 1, p.14, pp.1-13.
[14] Matthews, S. G., (1994), Partial metric topology, Annals of the New York Academy of Sciences, 728(1), pp.183-197.
[15] Musielak, J. and Orlicz, W., (1959), On modular spaces, Studia Mathematica, 18(1), pp.49-65.
[16] Nashine, H. K., Hadi Bonab, S., & Parvaneh, V. , (2023), (η, ψ)−Rational F-Contractions and Weak-Wardowski Contractions in a Triple-Controlled Modular-Type Metric Space, In advances in number theory and applied analysis, pp. 279-308.
[17] Pant, R., Shukla, R., Nashine, H. K. and Panicker, R., (2017), Some new fixed point theorems in partial metric spaces with applications, Journal of Function Spaces, 2017(1), p.1072750, pp.1-13.
[18] Paunovic, M. V., Bonab, S. H. and Parvaneh, V., (2023), Weak-Wardowski contractions in generalized triple-controlled modular metric spaces and generalized triple-controlled fuzzy metric spaces, In Soft Computing CRC Press pp. 45-66.
[19] Paunovic, M. V., Bonab, S. H., Parvaneh, V. and Golkarmanesh, F., (2023), Extended Parametric and Sequential Extended Fuzzy b-Metrics with an Application in Integral Equations, In Soft Computing CRC Press pp.15-28.
[20] Sarma, A., Goswami, N. and Das, D., (2019), Common fixed point result in C∗-algebra valued modular metric spaces with an application, Advances and Application in Mathematical Sciences, 19(1), pp.1-20.
[21] Shukla, S. and Radenovic, S., (2013), Some Common Fixed Point Theorems for F-Contraction Type Mappings in 0-Complete Partial Metric Spaces, Journal of Mathematics, 2013(1), p.878730, pp.1-7.
[22] Wardowski, D., (2012), Fixed points of a new type of contractive mappings in complete metric spaces, Fixed point theory and applications, 2012, p.94, pp.1-6.
[23] Wardowski, D., (2018), Solving existence problems via F-contractions, Proceedings of the american mathematical society, 146(4), pp.1585-1598.

Details

Primary Language

English

Subjects

Operator Algebras and Functional Analysis, Topology

Journal Section

Research Article

Authors

Santanu Narzary This is me
0000-0001-5611-1875
India

Liza Hazarika
0009-0006-7709-4705
India

Dipankar Das ^*
0000-0002-7430-1864
India

Publication Date

July 4, 2026

Submission Date

April 30, 2025

Acceptance Date

October 10, 2025

Published in Issue

Year 2026 Volume: 16 Number: 7

IZ

https://izlik.org/JA53TB25GE

Cite

RIS / Bibtex

APA

Narzary, S., Hazarika, L., & Das, D. (2026). $(\psi, \mathcal{GF})$-CONTRACTION MAPPINGS AND RELATED FIXED POINT RESULTS IN PARTIAL MODULAR METRIC SPACES. TWMS Journal of Applied and Engineering Mathematics, 16(7), 825-836. https://izlik.org/JA53TB25GE

AMA

1.Narzary S, Hazarika L, Das D. $(\psi, \mathcal{GF})$-CONTRACTION MAPPINGS AND RELATED FIXED POINT RESULTS IN PARTIAL MODULAR METRIC SPACES. JAEM. 2026;16(7):825-836. https://izlik.org/JA53TB25GE

Chicago

Narzary, Santanu, Liza Hazarika, and Dipankar Das. 2026. “$(\psi, \mathcal{GF})$-CONTRACTION MAPPINGS AND RELATED FIXED POINT RESULTS IN PARTIAL MODULAR METRIC SPACES”. TWMS Journal of Applied and Engineering Mathematics 16 (7): 825-36. https://izlik.org/JA53TB25GE.

EndNote

Narzary S, Hazarika L, Das D (July 1, 2026) $(\psi, \mathcal{GF})$-CONTRACTION MAPPINGS AND RELATED FIXED POINT RESULTS IN PARTIAL MODULAR METRIC SPACES. TWMS Journal of Applied and Engineering Mathematics 16 7 825–836.

IEEE

[1]S. Narzary, L. Hazarika, and D. Das, “$(\psi, \mathcal{GF})$-CONTRACTION MAPPINGS AND RELATED FIXED POINT RESULTS IN PARTIAL MODULAR METRIC SPACES”, JAEM, vol. 16, no. 7, pp. 825–836, July 2026, [Online]. Available: https://izlik.org/JA53TB25GE

ISNAD

Narzary, Santanu - Hazarika, Liza - Das, Dipankar. “$(\psi, \mathcal{GF})$-CONTRACTION MAPPINGS AND RELATED FIXED POINT RESULTS IN PARTIAL MODULAR METRIC SPACES”. TWMS Journal of Applied and Engineering Mathematics 16/7 (July 1, 2026): 825-836. https://izlik.org/JA53TB25GE.

JAMA

1.Narzary S, Hazarika L, Das D. $(\psi, \mathcal{GF})$-CONTRACTION MAPPINGS AND RELATED FIXED POINT RESULTS IN PARTIAL MODULAR METRIC SPACES. JAEM. 2026;16:825–836.

MLA

Narzary, Santanu, et al. “$(\psi, \mathcal{GF})$-CONTRACTION MAPPINGS AND RELATED FIXED POINT RESULTS IN PARTIAL MODULAR METRIC SPACES”. TWMS Journal of Applied and Engineering Mathematics, vol. 16, no. 7, July 2026, pp. 825-36, https://izlik.org/JA53TB25GE.

Vancouver

1.Santanu Narzary, Liza Hazarika, Dipankar Das. $(\psi, \mathcal{GF})$-CONTRACTION MAPPINGS AND RELATED FIXED POINT RESULTS IN PARTIAL MODULAR METRIC SPACES. JAEM [Internet]. 2026 Jul. 1;16(7):825-36. Available from: https://izlik.org/JA53TB25GE