Some Fixed Point Results on \((\alpha,\beta)\)-\(H\)-\(\varphi\)-Contraction Mappings in Partial Metric Spaces With Application

Authors

DOI:

https://doi.org/10.26713/cma.v15i1.2491

Keywords:

\(H\)-\(\varphi\)-contraction mapping, Generalized \(H\)-\(\varphi\)-contraction mapping, \((\alpha, \beta)\)-\(H\)-\(\varphi\)-contraction mapping, Partial metric spaces

Abstract

In this paper, we introduce the notion of \(H\)-\(\varphi\)-contraction, generalized \(H\)-\(\varphi\)-contraction,  \((\alpha,\beta)\)-\(H\)-\(\varphi\)-contraction mappings and establish some fixed point results for such mappings in the context of partial metric spaces. An example is presented to illustrate the validity of the results.\ Further, the existence of the solution of nonlinear integral equation is discussed as an application of the result.

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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. Aydi and E. Karapinar, A fixed point result for Boyd-Wong cyclic contractions in partial metric spaces, International Journal of Mathematics and Mathematical Sciences 2012 (2012), Article ID 597074, 11 pages, DOI: 10.1155/2012/597074.

D.W. Boyd and J. S.W.Wong, On nonlinear contractions, Proceedings of the American Mathematical Society 20 (1969), 458 – 464, DOI: 10.1090/S0002-9939-1969-0239559-9.

S. Chandok, Some fixed point theorems for (α,β)-admissible Geraghty type contractive mappings and related results, Mathematical Sciences 9 (2015), 127 – 135, DOI: 10.1007/s40096-015-0159-4.

S. Chandok, D. Kumar and M. S. Khan, Some results in partial metric space using auxiliary functions, Applied Mathematics E-Notes 15 (2015), 233 – 242, URL: https://www.kurims.kyoto-u.ac.jp/EMIS/journals/AMEN/2015/AMEN-150228.pdf.

D. Ili´c, V. Pavlovi´c and V. Rakoˇcevi´c, Some new extensions of Banach’s contraction principle to partial metric space, Applied Mathematics Letters 24(8) (2011), 1326 – 1330, DOI: 10.1016/j.aml.2011.02.025.

M. Kir and H. Kiziltunc, Generalized fixed point theorems in partial metric spaces, European Journal of Pure and Applied Mathematics 9(4) (2016), 443 – 451, URL: https://ejpam.com/index.php/ejpam/article/view/2584.

S. Kumar and F. Nziku, Some fixed point theorems for Boyd and Wong type contraction mapping in ordered partial metric spaces with an application, Journal of Function Spaces 2022 (2022), Article ID 7591420, 9 pages, DOI: 10.1155/2022/7591420.

S. G. Matthews, Partial metric topology, Annals of the New York Academy of Sciences 728(1) (1994), 183 – 197, DOI: 10.1111/j.1749-6632.1994.tb44144.x.

A. A. Mebawondu and O. T. Mewomo, Some fixed point results for a modified F-contractions via a new type of (α,β)-cyclic admissible mappings in metric spaces, Bulletin of the Transilvania University of Bra¸sov 12(61) (2019), 77 – 94, DOI: 10.31926/but.mif.2019.12.61.1.7.

A. Mebawondu, C. Izuchukwu, K. Aremu and O. T. Mewomo, On some fixed point results for (α,β)-Berinde-ϕ-contraction mappings with applications, International Journal of Nonlinear Analysis and Applications 11(2) (2020), 363 – 378, DOI: 10.22075/IJNAA.2020.20635.2183.

F. Nziku and S. Kumar, Boyd andWong type fixed point theorems in partial metric spaces, Moroccan Journal of Pure and Applied Analysis 5(2) (2019), 251 – 262, DOI: 10.2478/mjpaa-2019-0018.

H. Piri and P. Kumam, Some fixed point theorems concerning F-contraction in complete metric spaces, Fixed Point Theory and Applications 2014 (2014), Article number: 210, DOI: 10.1186/1687-1812-2014-210.

V. L. Rosa and P. Vetro, Fixed points for Geraghty-Contractions in partial metric spaces, Journal of Nonlinear Sciences and Applications 7(1) (2014), 1 – 10, DOI: 10.22436/jnsa.007.01.01.

B. Samet, C. Vetro and P. Vetro, Fixed point theorems for α-ψ contractive type mappings, Nonlinear Analysis: Theory, Methods & Applications 75(4) (2012), 2154 – 2165, DOI: 10.1016/j.na.2011.10.014.

B. Singh and V. Sihag, Fixed point theorems for new type of mappings in metric spaces and application, Journal of International Academy of Physical Sciences 25(1) (2021), 11 – 24, URL: https://www.iaps.org.in/journal/index.php/journaliaps/article/view/53.

D. Wardowski, Fixed points of a new type of contractive mappings in complete metric spaces, Fixed Point Theory and Applications 2012 (2012), Article number: 94, DOI: 10.1186/1687-1812-2012-94.

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Published

24-04-2024
CITATION

How to Cite

Tiwari, H., & Padmavati. (2024). Some Fixed Point Results on \((\alpha,\beta)\)-\(H\)-\(\varphi\)-Contraction Mappings in Partial Metric Spaces With Application. Communications in Mathematics and Applications, 15(1), 133–144. https://doi.org/10.26713/cma.v15i1.2491

Issue

Vol. 15 No. 1 (2024)

Section

Research Article

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