Some Fixed Point Theorems for \((\alpha,\beta,z)\)-Contraction Mapping under Simulation Functions in Banach Space

Snehlata Dwivedi; Urmila Mishra; A.K. Dubey; M.D. Pandey

doi:10.26713/cma.v14i1.1828

Authors

Snehlata Dwivedi Department of Mathematics, Dr. C. V. Raman University, Kargi Road, Kota, Bilaspur, Chhattisgarh, India
Urmila Mishra Department of Mathematics, Vishwavidyalaya Engineering College, Lakhanpur-Ambikapur, Chhatisgarh, India https://orcid.org/0000-0003-4353-1269 (unauthenticated)
A.K. Dubey Department of Applied Mathematics, Bhilai Institute of Technology, Bhilai House, Durg, Chhattisgarh, India https://orcid.org/0000-0001-5831-3817 (unauthenticated)
M.D. Pandey Department of Applied Mathematics, Bhilai Institute of Technology, Bhilai House, Durg, Chhattisgarh, India https://orcid.org/0000-0003-3833-5247 (unauthenticated)

DOI:

https://doi.org/10.26713/cma.v14i1.1828

Keywords:

Banach space, Fixed point, \((\alpha ,\beta ,z)\)-admissible mapping, Simulation functions

Abstract

In this paper, we prove some fixed point results in the setting of a Banach space via a cyclic \((\alpha ,\beta ,z)\)-admissible mapping imbedded in simulation function. Our results extend and generalize some well known results in the existing literature.

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References

S. A. Alizadeh, F. Moradlou and P. Salimi, Some fixed point results for (α,β)-(ψ,φ)-contractive mappings, Filomat 28(3) (2014), 635 – 647, DOI: 10.2298/Fil1403635a.

H. H. Alsulami, E. Karapınar, F. Khojasteh and A.-F. Roldán-López-de-Hierro, A proposal to the study of contractions in quasi-metric spaces, Discrete Dynamics in Nature and Society 2014 (2014), Article ID 269286, DOI: 10.1155/2014/269286.

E. Ameer, M. Arshad, D. Y. Shin and S. Yun, Common fixed point theorems of generalized multivalued (ψ,φ)-contractions in complete metric spaces with application, Mathematics 7(2) (2019), 194, DOI: 10.3390/math7020194.

H. Argoubi, B. Samet and C. Vetro, Nonlinear contractions involving simulation functions in a metric space with a partial order, Journal of Nonlinear Sciences and Applications 8(6) (2015), 1082 – 1094, DOI: 10.22436/jnsa.008.06.18.

S.-H. Cho, Fixed point theorems for (α,β)-z-contractions in metric spaces, International Journal of Mathematical Analysis 13(4) (2019), 161 – 174, DOI: 10.12988/ijma.2019.9318.

E. Karapınar, Fixed point results via simulations functions, Filomt 30(8) (2016), 2343 – 2350, DOI: 10.2298/FIL1608343k.

F. Khojasteh, S. Shukla and S. Radenovic, A new approach to the study of fixed point theory for simulation functions, Filomat 29(6) (2015), 1189 – 1194, DOI: 10.2298/FIL1506189k.

T. Mani, R. Krishnakumar and D. Dhamodharan, Fixed point of (α,β,Z)-Contraction mapping under simulation functions in Banach space, Malaya Journal of Matematik 9(1) (2001), 745 – 750, DOI: 10.26637/MJM0901/0131.

A.-F. Roldán-López-de-Hierro, E. Karapınar, C. Roldán-López-de-Hierro and J. Martínez-Moreno, Coincidence point theorems on metric spaces via simulation functions, Journal of Computational and Applied Mathematics 275 (2015), 345 – 355, DOI: 10.1016/j.cam.2014.07.011.