International Journal of Nonlinear Analysis and Applications

Coincidence and common fixed point theorems for generalized αT-contraction via tri-simulation function with an application

Document Type : Research Paper

Author

Department of Mathematics, K.R.M.D.A.V. College, Nakodar-144040, Punjab, India

Abstract

In this manuscript, we introduce the concept of generalized $\alpha \mathcal{T}$-contractive pair of mappings with the assistance of a tri-simulation function and use this concept to establish some coincidence and common fixed point theorems via $\alpha$-permissible mapping. We also give an illustrative example which yields the main result. Also, many existing results in the frame of metric spaces are established. We also apply our main theorem to derive coincidence and common fixed point results  for $\alpha \mathcal{T}$-contractive mapping with the assistance of $\alpha$-permissible function.

Keywords

[1] H. Argoubi, B. Samet, and C. Vetro, Nonlinear contractions involving simulation functions in a metric space with a partial order, J. Nonlinear Sci. Appl. 8 (2015), 1082–1094.
[2] H. Aydi, A. Felhi, E. Karapinar, and F.A. Alojail, Fixed points on quasi-metric spaces via simulation functions and consequences, J. Math. Anal. 9 (2018), no. 2, 10–24.
[3] S. Banach, Sur les operations dans les ensembles abstraits et leur application aux equations itegrales, Fund. Math. 3 (1922), 133–181.
[4] S.H. Bonab, R. Abazari, A.B. Vakilabad, and H. Hosseinzadeh, Generalized metric spaces endowed with vector-valued metrics and matrix equations by tripled fixed point theorems, J. Inequal. Appl. 204 (2020), 1–16.
[5] S.H. Bonab, V. Parvaneh, H. Hosseinzadeh, A. Dinmohammadi, and B. Mohammadi, Some common fixed point results via α-series for a family of js-contraction type mappings, Fixed Point Theory and Fractional Calculus, Forum for Interdisciplinary Mathematics, Springer, Singapore, 2022.
[6] S.H. Bonab, H. Hosseinzadeh V. Parvaneh, N.A. Shotorbani, H. Aydi, and S.J. Ghoncheh, n-tuple fixed point theorems via α-series in C*-algebra-valued metric spaces with an application in integral equations, Int. J. Ind. Math. 15 (2023), no. 2, 95–105.
[7] S. Chandok, A. Chanda, L.K. Dey, M. Pavlovic, and S. Radenovic, Simulation functions and Geraghty type results, Bol. Soc. Paranaense Mat. 39 (2021), no. 1, 35–50.
[8] P. Debnath, H.M. Srivastava, K. Chakraborty, and P. Kumam, (η, ψ)-rational f-contractions and weak-Wardowski contractions in a triple-controlled modular-type metric space, Adv. Number Theory Appl. Anal., 2023, pp. 279-308.
[9] R. Gubran, W.M. Alfaqieh, and M. Imdad, Common fixed point results for α-admissible mappings via simulation function, J. Anal. 25 (2017), 281–290.
[10] S. Gubran, W.M. Alfaqih, and M. Imdad, Fixed point results via tri-simulation function, Ital. J. Pure Appl. Math. 45 (2021), 419–430.
[11] H. Hosseinzadeh, S.H. Bonab, and K.A. Sefidab, Some common fixed point theorems for four mapping in generalized metric spaces, Thai J. Math. 20 (2022), no. 1, 425–437.
[12] H. Hosseinzadeha, H. Isik, and S.H. Bonaba, n-tuple fixed point theorems via α-series on partially ordered cone metric spaces, Int. J. Nonlinear Anal. Appl. 13 (2022), no. 2, 3115–3126.
[13] E. Karapinar, Fixed points results via simulation functions, Filomat 30 (2016), no. 8, 2343–2350.
[14] F. Khojasteh, S. Shukla, and S. Radenovic, A new approach to the study of fixed point theory for simulation functions, Filomat 29 (2015), no. 6, 1189–1194.
[15] O. Popescu, Some new fixed point theorems for α-Geraghty contractive type maps in metric spaces, Fixed Point Theory Appl. 190 (2014), 1–12.
[16] A. Roldan, E. Karapinar, C. Roldan, and J. Martınez-Moreno, Coincidence point theorems on metric spaces via simulation functions, J. Comput. Appl. Math. 275 (2015), 345–355.
[17] B. Samet, C. Vetro, and P. Vetro, Fixed point theorem for (α−ψ)-contractive type mappings, Nonlinear Anal. 75 (2012), 2154–2165.
[18] Y. Talaei, S. Micula, H. Hosseinzadeh, and S. Noeiaghdam, A novel algorithm to solve nonlinear fractional quadratic integral equations, AIMS Math. 7 (2022), no. 7, 13237–13257.
International Journal of Nonlinear Analysis and Applications
Volume 16, Issue 4
April 2025
Pages 169-180
  • Receive Date: 24 November 2022
  • Revise Date: 17 February 2024
  • Accept Date: 19 March 2024