A New Fixed Point Theorem for Generalized \((\alpha, \psi)\)-Contraction Mapping of Quadratic Type With Applications

Authors

DOI:

https://doi.org/10.26713/cma.v15i1.2557

Keywords:

Fixed point, \((\alpha, \psi)\)-contraction, \(b\)-metric space

Abstract

In this paper, we acquaint generalized \((\alpha,\psi)\)-contraction mappings of quadratic type and establish common fixed point results in the setting of rectangular quasi \(b\)-metric spaces. Our results extend and generalize related fixed point results of Karapinar and Lakzian \((\alpha-\psi)\)-Contractive mappings on generalized quasi metric spaces, Journal of Function Spaces  2014 (2014), 914398, 7 pages), Alharbi et al.~(\(\alpha\)-Contractive mappings on rectangular \(b\)-metric spaces and an application to integral equations, Journal of Mathematical Analysis 9(3) (2018), 47 - 60), and Khuangsatung et al. (The rectangular quasi-metric space and common fixed point theorem for \(\psi\)-contraction and \(\psi\)-Kannan mappings, Thai Journal of Mathematics (Special Issue (2020): Annual Meeting in Mathematics 2019), (2020), 89 - 101). We applied our result to facilitate the existence of a solution to an integral equation.

Downloads

Download data is not yet available.

References

M. Abbas, B.T. Leyew and S.H. Khan, A new Φ-generalized quasi metric space with some fixed point results and applications, Filomat, 31(11) (2017), 3157 – 172, DOI: 10.2298/FIL1711157A.

A. Abodayeh, W. Shatanawi and D. Turkoglu, Some fixed point theorems in quasi-metric spaces under quasi weak contraction, Global Journal of Pure and Applied Mathematics, 12 (2016), 4771 – 4780.

N. Alharbi, H. Aydi, A. Felhi, C. Özel and S. Sahmim, α-Contractive mappings on rectangular b-metric spaces and an application to integral equations, Journal of Mathematical Analysis, 9(3) (2018), 47–60, http://www.ilirias.com/jma/repository/docs/JMA9-3-5.pdf.

H. Aydi, E. Karapinar and B. Samet, Fixed points for generalized (α,ψ)-contractions on generalized metric spaces, Journal of Inequalities and Applications 2014 (2014), Article number: 229, DOI: 10.1186/1029-242X-2014-229.

H. Aydi, E. Karpinar and H. Lakzian, Fixed point results on a class of generalized metric spaces, Mathematical Sciences, 6 (2012), article number: 46, DOI: 10.1186/2251-7456-6-46.

S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales, Fundamenta Mathematicae, 3 (1922), 133 – 181, URL: https://eudml.org/doc/213289.

M. Berzig, E. Karapinar and A.F. Roldán-López-de-Hierro, Some fixed point theorems in Branciari metric spaces, Mathematica Slovaca 67(5) (2017), 1189 – 1202, DOI: 10.1515/ms-2017-0042.

A.A. Branciari, A fixed point theorems of Banach-Caccioppoli type on a class of generalized metric spaces, Publicationes Mathematicae Debrecen 57(1-2) (2000), 31 – 37, URL: https://publi.math.unideb.hu/load_doc.php?p=617&t=pap.

V. Cvetkovi´c, E. Karpinar and V. Rakocevic, Some fixed point results on quasi-b-metric-like-spaces, Journal of Inequalities and Applications 2015 (2015), Article number: 374, DOI: 10.1186/s13660-015-0897-8.

S. Czerwik, Contraction mapping in b-metric spaces, Acta Mathematica et Informatica Universitatis Ostraviensis 1(1) (1993), 5 – 11, URL: http://dml.cz/dmlcz/120469.

H.S. Ding, V. Ozturk and S. Radenovic, On some new fixed point results in b-metric spaces, Journal of Nonlinear Science and Applications 8(4) (2015), 378 – 386, DOI: 10.22436/jnsa.008.04.10.

R. George, S. Radenovi´c, K.P. Reshma and S. Shukla, Rectangular b-metric space and contraction principle, Journal of Nonlinear Science and Applications 8(6) (2015), 1005 – 1013, DOI: 10.22436/jnsa.008.06.11.

E. Karapinar, On (α,ψ) contractions of integral type on generalized metric spaces, In: Current Trends in Analysis and Its Application, V. Mityushev and M. Ruzhansky (editors), (2015), 843 – 854, Birkhäuser, Cham., DOI: 10.1007/978-3-319-12577-0_91.

E. Karapinar, S. Czerwik and H. Aydi, (α,ψ)-Meir-Keeler contraction mappings in generalized b-metric spaces, Journal of Function Spaces 2018 (2018), 3264620, 4 pages, DOI: 10.1155/2018/3264620.

E. Karapinar and H. Lakzian, (α−ψ)-Contractive mappings on generalized quasi metric spaces, Journal of Function Spaces 2014 (2014), 914398, 7 pages, DOI: 10.1155/2014/914398.

W. Khuangsatung, S. Chan-Iam, P. Muangkarn and C. Suanoom, The rectangular quasi-metric space and common fixed point theorem for ψ-contraction and ψ-Kannan mappings, Thai Journal of Mathematics (Special Issue (2020): Annual Meeting in Mathematics 2019), (2020), 89 – 101, https://thaijmath2.in.cmu.ac.th/index.php/thaijmath/article/view/958.

H. Lakzian and B. Samet, Fixed points for (ψ,φ)-weakly contractive mappings in generalized metric spaces, Applied Mathematics Letters 25(5) (2012), 902 – 906, DOI: 10.1016/j.aml.2011.10.047.

H. Lakzian, S. Barootkoob, N. Mlaiki, H. Aydi and M. De la Sen, On generalized (α,ψ,MΩ)- contraction with w-distances and an application to nonlinear Fredholm integral equations, Symmetry 11(8) (2019), 982, DOI: 10.3390/sym11080982.

I.-J. Lin, C.M. Chen and E. Karapinar, Periodic points of weaker Meir-Keeler contractive mappings on generalized quasimetric spaces, Abstract and Applied Analysis 2014 (2014), Article ID 490450, 6 pages, DOI: 10.1155/2014/490450.

H.K. Nashine and H. Lakzian, Periodic points of weaker Meir-Keeler function in complete generalized metric spaces, Filomat 30(8) (2016), 2191 – 2206, DOI: 10.2298/FIL1608191N.

V. Ozturk, Fixed point theorems in b-rectangular metric spaces, Universal Journal of Mathematics and Applications 3(1) (2020), 28 – 32, DOI: 10.32323/ujma.609715.

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.

M.H. Shah and N. Hussain, Nonlinear contractions in partially ordered quasi b-metric spaces, Communications of the Korean Mathematical Society 27(1) (2012), 117 – 128, DOI: 10.4134/CKMS.2012.27.1.117.

Downloads

Published

24-04-2024
CITATION

How to Cite

Tiwari, R., & Sharma, N. (2024). A New Fixed Point Theorem for Generalized \((\alpha, \psi)\)-Contraction Mapping of Quadratic Type With Applications. Communications in Mathematics and Applications, 15(1), 445–461. https://doi.org/10.26713/cma.v15i1.2557

Issue

Vol. 15 No. 1 (2024)

Section

Research Article

License

Creative Commons Licence 4.0 by  

Authors who publish with this journal agree to the following terms:

  • Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a CCAL that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
  • Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
  • Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.