On Some Fixed Point Results for Cyclic \((\alpha,\beta)\)-admissible Almost z-Contraction in Metric-Like Space with Simulation Function

Snehlata Mishra; Anil Kumar Dubey; Urmila Mishra; R. P. Dubey

doi:10.26713/cma.v13i1.1666

Authors

Snehlata Mishra Department of Mathematics Dr. C.V. Raman University, Kargi Road Kota, Bilaspur (Chhattisgarh), India
Anil Kumar Dubey Department of Mathematics, Bhilai Institute of Technology, Bhilai House, Durg (Chhattisgarh), India https://orcid.org/0000-0001-5831-3817 (unauthenticated)
Urmila Mishra Department of Mathematics, Vishwavidyalaya Engineering College, Lakhanpur-Ambikapur (Chhattisgarh), India https://orcid.org/0000-0003-4353-1269 (unauthenticated)
R. P. Dubey Department of Mathematics Dr. C.V. Raman University, Kargi Road Kota, Bilaspur (Chhattisgarh), India

DOI:

https://doi.org/10.26713/cma.v13i1.1666

Keywords:

Metric-like space, Fixed point, Simulation function, Cyclic \((\alpha,\beta)\)-admissible almost z-contraction

Abstract

In this paper, we present some fixed point results in the setting of metric-like space by defining a cyclic \((\alpha,\beta)\)-admissible almost z-contraction embedded in simulation function. Suitable examples are also established to verify the validity of the results obtained.

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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, 10 pages, DOI: 10.1155/2014/269286.

A. Amini-Harandi, Metric-like spaces, partial metric spaces and fixed points, Fixed Point Theory and Applications 2012 (2012), Article number: 204, URL: http://www.fixedpointtheoryandapplications.com/content/2012/1/204.

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.

H. Aydi and A. Felhi, Best proximity points for cyclic Kannan-Chatterjea-Ciric type contractions on metric-like spaces, Journal of Nonlinear Sciences and Applications 9(5) (2016), 2458 – 2466, DOI: 10.22436/jnsa.009.05.45.

H. Aydi, A. Felhi and H. Afshari, New Geraghty type contractions on metric-like spaces, Journal of Nonlinear Sciences and Applications 10(2) (2017), 780 – 788, DOI: 10.22436/jnsa.010.02.38.

H. Aydi, A. Felhi and S. Sahmim, Fixed points of multivalued nonself almost contractions in metric-like spaces, Mathematical Sciences 9 (2015), 103 – 108, DOI: 10.1007/s40096-015-0156-7.

G.V.R. Babu, M.L. Sandhya and M.V.R. Kameswari, A note on a fixed point theorem of Berinde on weak contractions, Carpathian Journal of Mathematics 24(1) (2008), 8 – 12, URL: https://www.jstor.org/stable/43996834.

V. Berinde, Approximating fixed Point of weak contractions using the Picard iteration, Nonlinear Analysis Forum 9(1) (2004), 43 – 53.

V. Berinde, General constructive fixed point theorems for Ciric-type almost contractions in metric spaces, Carpathian Journal of Mathematics 24(2) (2018), 10 – 19, URL: https//www.jstor.org/stable/43996855.

A. Felhi, H. Aydi and D. Zhang, Fixed points for α-admissible contractive mappings via simulation functions, Journal of Nonlinear Sciences and Application 9(10) (2016), 5544 – 5560, DOI: 10.22436/jnsa.009.10.05.

P. Hitzler and A.K. Seda, Dislocated topologies, Journal of Electrical Engineering 51(12) (2000), 1 – 12, URL: https//corescholar.libraries.wright.edu/cse/15.

H. Isik, N.B. Gungor, C. Park and S.Y. Jang, Fixed point theorems for almost z-contractions with an application, Mathematics 6(3) (2018), 37, DOI: 10.3390/math6030037.

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

H. Qawaqneh, New contraction embedded with simulation function and cyclic (α,β)-admissible in metric like spaces, International Journal of Mathematics and Computer Science 15(4) (2020), 1029 – 1044, URL: http://ijmcs.future-in-tech.net/15.4/R-HaithamQawaqneh.pdf.

H. Qawaqneh, M.S.M. Noorani, W. Shatanawi, K. Abodayeh and H. Alsamir, Fixed point for mappings under contractive condition based on simulation functions and cyclic (α,β)-admissibility, Journal of Mathematical Analysis 9(1) (2018), 38 – 51, URL: www.ilirias.com/jma/repository/docs/JMA9-1-4.pdf.

H.A. Qawaqneh, M.S. Noorani and W. Shatanawi, Fixed point for results for Geraghty type generalized F-contraction for weak α-admissible mapping in metric-like spaces, European Journal of Pure and Applied Mathematics 11(3) (2018), 702 – 716, DOI: 10.29020/nybg.ejpam.v11i3.3294.

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.