A note on three different contractions in partially ordered complex valued $ G_b $-metric spaces

Yiquan Li; Chuanxi Zhu; Yingying Xiao; Li Zhou; Yiquan Li; Chuanxi Zhu; Yingying Xiao; Li Zhou

doi:10.3934/math.2022684

AIMS Mathematics

2022, Volume 7, Issue 7: 12322-12341. doi: 10.3934/math.2022684

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Research article

A note on three different contractions in partially ordered complex valued $ G_b $-metric spaces

1.
School of Mathematics and Computer Sciences, Nanchang University, Nanchang, Jiangxi, 330031, China
2.
Department of Basic discipline, Nanchang JiaoTong Institute, Nanchang, Jiangxi, 330031, China

Received: 01 March 2022 Revised: 09 April 2022 Accepted: 19 April 2022 Published: 25 April 2022
MSC : 47H10, 54H25, 54D99, 54E99

In this paper, we introduce the complex valued $ C^{p} $-class function, a type of Geraghty contraction and a type of JS contraction in complete partially ordered complex valued $ G_b $-metric spaces, prove three fixed point theorems in this space, and also we give some examples to support our results.
- complex valued $ G_b $-metric space,
- complex valued $ C^{p} $-class function,
- Geraghty contraction,
- JS contraction,
- partially ordered
Citation: Yiquan Li, Chuanxi Zhu, Yingying Xiao, Li Zhou. A note on three different contractions in partially ordered complex valued $ G_b $-metric spaces[J]. AIMS Mathematics, 2022, 7(7): 12322-12341. doi: 10.3934/math.2022684

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Abstract

In this paper, we introduce the complex valued $ C^{p} $-class function, a type of Geraghty contraction and a type of JS contraction in complete partially ordered complex valued $ G_b $-metric spaces, prove three fixed point theorems in this space, and also we give some examples to support our results.

References

[1]	Z. Mustafa, B. Sims, A new approach to generalized metric spaces, J. Nonlinear Convex A., 7 (2006), 289-297.
[2]	A. Aghajani, M. Abbas, J. R. Roshan, Common fixed point of generalized weak contractive mappings in partially ordered $G_b$-metric spaces, Filomat, 28 (2014), 1087-1101. http://dx.doi.org/10.2298/FIL1406087A doi: 10.2298/FIL1406087A
[3]	L. Zhu, C. X. Zhu, C. F. Chen, Common fixed point theorems for fuzzy mappings in $G$-metric spaces, Fixed Point Theory A., 2012 (2012), 159. http://dx.doi.org/10.1186/1687-1812-2012-159 doi: 10.1186/1687-1812-2012-159
[4]	M. Asadi, E. Karapınar, P. Salimi, A new approach to $G$-metric and related fixed point theorems, J. Inequal. Appl., 2013 (2013), 454. http://dx.doi.org/10.1186/1029-242X-2013-454 doi: 10.1186/1029-242X-2013-454
[5]	J. R. Roshan, N. Shobkolaei, S. Sedghi, V. Parvaneh, S. Radenovi$\acute{c}$, Common fixed point theorems for three maps in discontinuous $G_b$-metric spaces, Acta Math. Sci., 34 (2014), 1643-1654. http://dx.doi.org/10.1016/S0252-9602(14)60110-7 doi: 10.1016/S0252-9602(14)60110-7
[6]	J. Chen, C. X. Zhu, L. Zhu, A note on some fixed point theorems on $G$-metric spaces, J. Appl. Anal. Comput., 11 (2021), 101-112. http://dx.doi.org/10.11948/20190125 doi: 10.11948/20190125
[7]	Y. U. Gaba, Fixed point theorems in $G$-metric spaces, J. Math. Anal. Appl., 455 (2017), 528-537. http://dx.doi.org/10.1016/j.jmaa.2017.05.062 doi: 10.1016/j.jmaa.2017.05.062
[8]	M. Liang, C. X. Zhu, C. F. Chen, Z. Q. Wu, Some new theorems for cyclic contractions in $G_b$-metric spaces and some applications, Appl. Math. Comput., 346 (2019), 545-558. http://dx.doi.org/10.1016/j.amc.2018.10.028 doi: 10.1016/j.amc.2018.10.028
[9]	C. X. Zhu, J. Chen, C. F. Chen, J. H. Chen, H. P. Huang, A new generalization of $\mathcal{F}$-metric spaces and some fixed point theorems and an application, J. Appl. Anal. Comput., 11 (2021), 2649-2663. http://dx.doi.org/10.11948/20210244 doi: 10.11948/20210244
[10]	C. X. Zhu, J. Chen, X. J. Huang, J. H. Chen, Fixed point theorems in modular spaces with simulation functions and altering distance functions with applications, J. Nonlinear Convex A., 2020, 1403-1424.
[11]	Y. X. Wang, C. F. Chen, Two new Geraghty type contractions in $G_b$-metric spaces, J. Funct. Space., 2019 (2019). http://dx.doi.org/10.1155/2019/7916486
[12]	M. Jleli, E. Karapınar, B. Samet, Further generalizations of the Banach contraction principle, J. Inequal. Appl., 2014 (2014), 439. http://dx.doi.org/10.1186/1029-242X-2014-439 doi: 10.1186/1029-242X-2014-439
[13]	H. Aydi, A. Felhi, H. Afshari, New Geraghty type contractions on metric-like spaces, J. Nonlinear Sci. Appl., 10 (2017), 780-788. http://dx.doi.org/10.22436/jnsa.010.02.38 doi: 10.22436/jnsa.010.02.38
[14]	M. Jleli, B. Samet, A new generalization of the Banach contraction principle, J. Inequal. Appl., 2014 (2014), 38. http://dx.doi.org/10.1186/1029-242X-2014-38 doi: 10.1186/1029-242X-2014-38
[15]	A. Shoaib, M. Arshad, T. Rasham, M. Abbas, Unique fixed point results on closed ball for dislocated quasi $G$-metric spaces, T. A. Razmadze Math. In., 171 (2017), 221-230. http://dx.doi.org/10.1016/j.trmi.2017.01.002 doi: 10.1016/j.trmi.2017.01.002
[16]	O. Ege, Complex valued $G_b$-metric spaces, J. Comput. Anal. Appl., 21 (2016), 363-368.
[17]	O. Ege, Some fixed point theorems in complex valued $G_b$-metric spaces, J. Nonlinear Convex A., 18 (2017), 1997-2005.
[18]	O. Ege, C. Park, A. H. Ansari, A different approach to complex valued $G_b$-metric spaces, Adv. Differ. Equ., 2020 (2020), 152. http://dx.doi.org/10.1186/s13662-020-02605-0 doi: 10.1186/s13662-020-02605-0
[19]	O. Ege, I. Karaca, Common fixed point results on complex valued $G_b$-metric spaces, Thai J. Math., 16 (2018), 775-787.
[20]	A. H. Ansari, O. Ege, S. Radenovi$\acute{c}$, Some fixed point results on complex valued $G_b$-metric spaces, RACSAM Rev. R. Acad. A, 112 (2018), 463-472. http://dx.doi.org/10.1007/s13398-017-0391-x doi: 10.1007/s13398-017-0391-x
[21]	H. Afshari, Solution of fractional differential equations in quasi-$b$-metric and $b$-metric-like spaces, Adv. Differ. Equ., 2019 (2019), 285. http://dx.doi.org/10.1186/s13662-019-2227-9 doi: 10.1186/s13662-019-2227-9
[22]	H. Afshari, M. Atapour, E. Karapınar, A discussion on a generalized Geraghty multi-valued mappings and applications, Adv. Differ. Equ., 2020 (2020). http://dx.doi.org/10.1186/s13662-020-02819-2
[23]	H. Afshari1, S. Kalantari, D. Baleanu, Solution of fractional differential equations via $\alpha$-$\psi$-Geraghty type mappings, Adv. Differ. Equ., 2018 (2018), 347. https://doi.org/10.1186/s13662-018-1807-4 doi: 10.1186/s13662-018-1807-4
[24]	M. Jleli, B. Samet, Remarks on $G$-metric spaces and fixed point theorems, Fixed Point Theory A., 2012 (2012), 210. http://dx.doi.org/10.1186/1687-1812-2012-210 doi: 10.1186/1687-1812-2012-210
[25]	R. P. Agarwal, H. H. Alsulami, E. Karapınar, F. Khojasteh, Remarks on some recent fixed point results on quaternion-valued metric spaces, Abstr. Appl. Anal., 2014 (2014). http://dx.doi.org/10.1155/2014/171624
[26]	A. Shoaib, S. Mustafa, A. Shahzad, Common fixed point of multivalued mappings in ordered dislocated quasi $G$-metric spaces, Punjab Univ. J. Math., 52 (2020).
[27]	A. E. Al-Mazrooei, A. Shoaib, J. Ahmad, Unique fixed-point results for $\beta$-admissible mapping under ($\beta$-$\check{\psi}$)-contraction in complete dislocated $G_d$-metric space, Mathematics, 8 (2020). http://dx.doi.org/10.3390/math8091584
[28]	M. Abbas, S. Z. Németh, Finding solutions of implict complementarity problems by isotonicty of the metric projection, Nonlinear Anal., 75 (2012), 2349-2361. http://dx.doi.org/10.1016/j.na.2011.10.033 doi: 10.1016/j.na.2011.10.033

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