# Fixed-point theorems for ($\phi,\psi$,$\beta$)-Geraghty contraction type mappings in partially ordered fuzzy metric spaces with applications

## Main Article Content

## Abstract

## Article Details

This work is licensed under a Creative Commons Attribution-NonCommercial 3.0 Unported License.

## References

[1] I. Altun, H. Simsek, Some fixed point theorems on ordered metric spaces and application, Fixed Point Theory Appl. 2010 (2010), 1–17. Google Scholar

[2] S. Chandok, Some fixed point theorems for (α, β)-admissible Geraghty type contractive mappings and related results, Math Sci. 9 (2015), 127–135. Google Scholar

[3] Y. J. Cho, T. M. Rassias, R. Saadati, Fixed Point Theorems in Partially Ordered Fuzzy Metric Spaces, Fuzzy Operator Theory in Mathematical Analysis 2018 (2018), 177–261. Google Scholar

[4] A. George, P. Veeramani, On some results in fuzzy metric spaces, Fuzzy Set Syst. 64 (1994), 395–399. Google Scholar

[5] M. Geraghty: On contractive mappings, Proc. Amer. Math. Soc. 40 (1973), 604–608. Google Scholar

[6] M. E. Gordji, M. Ramezani, Y. J. Cho, S. Pirbavafa, A generalization of Geraghty’s theorem in partially ordered metric spaces and applications to ordinary differential equations, Fixed Point Theory Appl. 2012 (2012), 1–74. Google Scholar

[7] N. Goswami, B. Patir, Fixed point theorems in fuzzy metric spaces for mappings with Bγ, μ condition, Proyecciones 40 (4) (2021), 837–857. Google Scholar

[8] N. Goswami, B. Patir, Some applications of fixed point theorem in fuzzy boundary value problems, Advances in Science and Technology 2 (2020), 108–114. Google Scholar

[9] N. Goswami, B. Patir, Fixed point theorems for asymptotically regular mappings in fuzzy metric spaces, Korean J. Math. 27 (4) (2019), 861–877. Google Scholar

[10] M. Grabiec, Fixed points in fuzzy metric spaces, Fuzzy Set Syst. 27 (1988), 385–389. Google Scholar

[11] V. Gregori, S. Morillas, A. Sapena, Examples of fuzzy metrics and applications, Fuzzy Set Syst. 170 (2011), 95–111. Google Scholar

[12] V. Gupta, W. Shatanawi, N. Mani, Fixed point theorems for (ψ,β)-Geraghty contraction type maps in ordered metric spaces and some applications to integral and ordinary differential equations, J. Fixed Point Theory Appl. 19 (2017), 1251–1267. Google Scholar

[13] A. A. Harandi, H. Emami, A fixed point theorem for contraction type maps in partially ordered metric spaces and application to ordinary different equations, Nonlinear Analysis 72 (2010), 2238–2242. Google Scholar

[14] J. Harjani, K. Sadarangani, Fixed point theorems for weakly contractive mappings in partially ordered sets, Nonlinear Analysis 71 (2009), 3403–3410. Google Scholar

[15] N. Mlaiki, U. C ̧elik, N. Ta ̧s, N. Y. O ̈zgu ̈r, A. Mukheimer, Wardowski type contractions and the fixed-circle problem on s-metric spaces, J. Math. 2018 (2018), 1–9. Google Scholar

[16] J. J. Nieto, R. R. Lopez, Applications of contractive-like mapping principles to fuzzy equations, Rev. Mat. Complut. 19 (2) (2006), 361–383. Google Scholar

[17] N. Y. O ̈zgu ̈r and N. Ta ̧s, Some fixed-circle theorems on metric spaces, Bull. Malays. Math. Sci. Soc. 42 (4) (2019), 1433–1449. Google Scholar

[18] B. Patir, N. Goswami, L. N. Mishra, Fixed point theorems in fuzzy metric spaces for mappings with some contractive type conditions, Korean J. Math. 26 (2) (2018), 307–326. Google Scholar

[19] Y. Shen, D. Qiu, W. Chen, Fixed point theorems in fuzzy metric spaces, Appl. Math. Lett. 25 (2012), 138–141. Google Scholar

[20] R. L. Herman, Introduction to Partial Differential Equations, (2014). http://people.uncw. edu/hermanr/pde1/PDEbook/Green.pdf Google Scholar

[21] L. R. Williams, R. W. Leggett, Multiple fixed point theorems for problems in chemical reactor theory, J. Math. Anal. Appl. 69 (1) (1979), 180–193. Google Scholar