Discussion on the hybrid Jaggi-Meir-Keeler type contractions

Erdal Karapınar; Andreea Fulga; Erdal Karapınar; Andreea Fulga

doi:10.3934/math.2022703

AIMS Mathematics

2022, Volume 7, Issue 7: 12702-12717. doi: 10.3934/math.2022703

Previous Article Next Article

Research article

Discussion on the hybrid Jaggi-Meir-Keeler type contractions

Erdal Karapınar ^1,2,3,
Andreea Fulga ^{4
,
,}

1.
Division of Applied Mathematics, Thu Dau Mot University, Thu Dau Mot City 820000, Binh Duong Province, Vietnam
2.
Department of Mathematics, Çankaya University, 06790, Etimesgut, Ankara, Turkey
3.
Department of Medical Research, China Medical University Hospital, China Medical University, 40402, Taichung, Taiwan
4.
Department of Mathematics and Computer Sciences, Transilvania University of Brasov, Brasov, Romania

Received: 01 March 2022 Revised: 01 April 2022 Accepted: 12 April 2022 Published: 29 April 2022
MSC : 47H10, 54H25

In this paper, the notion of hybrid Jaggi-Meir-Keeler type contraction is introduced. The existence of a fixed point for such operators is investigated. The derived results combine and extend a number of existing results in the corresponding literature. Examples are established to express the validity of the obtained results.
- Jaggi contraction,
- Meir-Keeler contraction,
- Hyprid contraction,
- fixed point
Citation: Erdal Karapınar, Andreea Fulga. Discussion on the hybrid Jaggi-Meir-Keeler type contractions[J]. AIMS Mathematics, 2022, 7(7): 12702-12717. doi: 10.3934/math.2022703

Related Papers:

Abstract

In this paper, the notion of hybrid Jaggi-Meir-Keeler type contraction is introduced. The existence of a fixed point for such operators is investigated. The derived results combine and extend a number of existing results in the corresponding literature. Examples are established to express the validity of the obtained results.

References

[1]	S. Banach, Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales (France), Fund. Math., 3 (1922) 133–181.
[2]	A. Meir, E. Keeler, A theorem on contraction mappings, J. Math. Anal. Appl., 28 (1969), 326–329. http://dx.doi.org/10.1016/0022-247X(69)90031-6 doi: 10.1016/0022-247X(69)90031-6
[3]	D. Jaggi, Some unique fixed point theorems, Indian. J. Pure. Appl. Math., 8 (1977), 223–230.
[4]	E. Karapınar, Revisiting the Kannan type contractions via interpolation, Advances in the Teory of Nonlinear Analysis and its Application, 2 (2018), 85–87. http://dx.doi.org/10.31197/atnaa.431135 doi: 10.31197/atnaa.431135
[5]	R. Bisht, V. Rakoćević, Generalized Meir-Keeler type contractions and discontinuity at fixed point, Fixed Point Theory, 19 (2018), 57–64. http://dx.doi.org/10.24193/fpt-ro.2018.1.06 doi: 10.24193/fpt-ro.2018.1.06
[6]	R. Kannan, Some results on fixed points, Bull. Cal. Math. Soc., 60 (1968), 71–76.
[7]	E. Karapınar, R. Agarwal, H. Aydi, Interpolative Reich-Rus-Ćirić type contractions on partial metric spaces, Mathematics, 6 (2018), 256. http://dx.doi.org/10.3390/math6110256 doi: 10.3390/math6110256
[8]	H. Aydi, E. Karapınar, A. Roldan Lopez de Hierro, $\omega$-interpolative Ćirić-Reich-Rus-type contractions, Mathematics, 7 (2019), 57. http://dx.doi.org/10.3390/math7010057 doi: 10.3390/math7010057
[9]	E. Karapınar, H. Aydi, Z. Mitrovic, On interpolative Boyd-Wong and Matkowski type contractions, TWMS J. Pure Appl. Math., 11 (2020), 204–212.
[10]	H. Aydi, C. Chen, E. Karapınar, Interpolative Ciric-Reich-Rus type contractions via the Branciari distance, Mathematics, 7 (2019), 84. http://dx.doi.org/10.3390/math7010084 doi: 10.3390/math7010084
[11]	M. Nazam, H. Aydi, A. Hussain, Generalized interpolative contractions and an application, J. Math., 2021 (2021), 6461477. http://dx.doi.org/10.1155/2021/6461477 doi: 10.1155/2021/6461477
[12]	O. Popescu, Some new fixed point theorems for $\alpha$-geraghty contraction type maps in metric spaces, Fixed Point Theory Appl., 2014 (2014), 190. http://dx.doi.org/10.1186/1687-1812-2014-190 doi: 10.1186/1687-1812-2014-190
[13]	E. Karapınar, B. Samet, Generalized ($\alpha-\psi$) contractive type mappings and related fixed point theorems with applications, Abstr. Appl. Anal., 2012 (2012), 793486. http://dx.doi.org/10.1155/2012/793486 doi: 10.1155/2012/793486
[14]	U. Aksoy, E. Karapınar, I. Erhan, Fixed points of generalized $\alpha$-admissible contractions on $b$-metric spaces with an application to boundary value problems, J. Nonlinear Convex A., 17 (2016), 1095–1108.
[15]	H. Aydi, E. Karapınar, H. Yazidi, Modified F-contractions via $\alpha$-admissible mappings and application to integral equations, Filomat, 31 (2017), 1141–1148. http://dx.doi.org/10.2298/FIL1705141A doi: 10.2298/FIL1705141A
[16]	H. Aydi, E. Karapınar, D. Zhang, A note on generalized admissible-Meir-Keeler-contractions in the context of generalized metric spaces, Results Math., 71 (2017), 73–92.
[17]	V. Todorĉević, Harmonic quasiconformal mappings and hyperbolic type metrics, Cham: Springer, 2019. http://dx.doi.org/10.1007/978-3-030-22591-9
[18]	P. Debnath, N. Konwar, S. Radenović, Metric fixed point theory: applications in science, engineering and behavioural sciences, Singapore: Springer, 2021. http://dx.doi.org/10.1007/978-981-16-4896-0
[19]	H. Huang, Y. Singh, M. Khan, S. Radenović, Rational type contractions in extended $b$-metric spaces, Symmetry, 13 (2021), 614. http://dx.doi.org/10.3390/sym13040614 doi: 10.3390/sym13040614

Reader Comments

Your name:*

Email:*
© 2022 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)