Some results on coupled coincidence points in vector quasi cone metric spaces over Banach algebras with satisfactory cones
Authors
S. M. A. Abou Bakr
- Department of Mathematics, Faculty of Science, Ain Shams University, Cairo, Egypt.
H. K. Hussein
- Department of Mathematics, Faculty of Science, Ain Shams University, Cairo, Egypt.
Abstract
Let \((X, C,\mathbb{D}_{C}, \chi )\) be a complete parametric vector quasi cone metric space over a Banach algebra \(\mathbb{A}\), \(C\) be a cone in \(\mathbb{A}\) that contains some semi-interior points, \(\chi\) be a metric parameter in \(C\) with a spectral radius \(\sigma (\chi )\geq 1\), and \(T: X\times X \to X\) be a generalized contraction mapping where its parametric contractions are vectors in \(C\), with these settings and without relying on the assumptions of normality and solidness of \(C\), we prove the existence of coupled coincidence points of the mapping \(T\) and hence generalize many theorems concerned with the existence of coupled coincidence points of such types and we support these results with some illustrative examples.
Share and Cite
ISRP Style
S. M. A. Abou Bakr, H. K. Hussein, Some results on coupled coincidence points in vector quasi cone metric spaces over Banach algebras with satisfactory cones, Journal of Mathematics and Computer Science, 31 (2023), no. 3, 305--317
AMA Style
Abou Bakr S. M. A., Hussein H. K., Some results on coupled coincidence points in vector quasi cone metric spaces over Banach algebras with satisfactory cones. J Math Comput SCI-JM. (2023); 31(3):305--317
Chicago/Turabian Style
Abou Bakr, S. M. A., Hussein, H. K.. "Some results on coupled coincidence points in vector quasi cone metric spaces over Banach algebras with satisfactory cones." Journal of Mathematics and Computer Science, 31, no. 3 (2023): 305--317
Keywords
- Banach algebra
- normal cones
- solid cones
- cone metric spaces over Banach algebra
- semi interior points
- coupled coincidence points
MSC
References
-
[1]
S. M. A. Abou Bakr, A study on common fixed point of joint (A; B) generalized cyclic - abc weak nonexpansive mappings and generalized cyclic abc ; r contractions in quasi metric spaces, Abstr. Appl. Anal., 2020 (2020), 10 pages
-
[2]
S. M. A. Abou Bakr, Cyclic G- -weak contraction-weak nonexpansive mappings and some fixed point theorems in metric spaces, Abstr. Appl. Anal., 2021 (2021), 9 pages
-
[3]
S. M. A. Abou Bakr, Theta Cone Metric Spaces and Some Fixed Point Theorems, J. Math., 2020 (2020), 7 pages
-
[4]
S. M. A. Abou Bakr, Coupled fixed-point theorems in theta-cone-metric spaces, J. Math., 2021 (2021), 7 pages
-
[5]
S. M. A. Abou Bakr, Coupled fixed point theorems for some type of contraction mappings in b-cone and b-theta cone metric spaces, J. Math., 2021 (2021), 9 pages
-
[6]
S. M. A. Abou Bakr, Fixed point theorems of generalized contraction mappings on $-cone metric spaces over Banach algebras, Rocky Mountain J. Math., 52 (2022), 757–776
-
[7]
S. M. A. Abou Bakr, On various types of cone metric spaces and some applications in fixed point theory, Int. J. Nonlinear Anal. Appl., 14 (2023), 163–184
-
[8]
R. P. Agarwal, W. Sintunavarat, P. Kumam, Coupled coincidence point and Common Coupled Fixed Point Theorems Lacking the mixed monotone property, Fixed Point Theory Appl., 2013 (2013), 20 pages
-
[9]
S. Aleksi´c, Z. Kadelburg, Z. D. Mitrovi´c, S. Radenovi´c,, A new survey: Cone metric spaces, J. Int. Math. Virtual Inst., 9 (2019), 93–121
-
[10]
S. M. Ali, Fixed point theorems of some type contraction mappings, J. Nonlinear Convex Anal., 14 (2013), 331–342
-
[11]
A. Alotaibi, S. M. Alsulami, Coupled coincidence points for monotone operators in partially ordered metric spaces, Fixed Point Theory Appl., 2011 (2011), 13 pages
-
[12]
A. Al-Rawashdeh, W. Shatanawi, M. Khandaqji, Normed ordered and E-metric spaces, Int. J. Math. Math. Sci., 2012 (2012), 11 pages
-
[13]
A. Amini-Harandi, M. Fakhar, Fixed point theory in cone metric spaces obtained via the scalarization method, Comput. Math. Appl., 59 (2010), 3529–3534
-
[14]
S. Banach, Sur les op´erations dans les ensembles abstraits et leur application aux ´equations int´egrales, Fund. Math., 3 (1922), 133–181
-
[15]
A. Basile, M. G. Graziano, M. Papadaki, I. A. Polyrakis, Cones with semi-interior points and equilibrium, J. Math. Econ., 71 (2017), 36–48
-
[16]
T. G. Bhaskar, V. Lakshmikantham, Fixed Point Theorems in Partially Ordered Metric Spaces and Applications, Nonlinear Anal., 65 (2006), 1379–1393
-
[17]
P. Borisut, P. Kumam, V. Gupta, N. Mani, Generalized ( , , )-Weak Contractions for Initial Value Problems, Mathematics, 7 (2019), 1–14
-
[18]
H. C¸ akallı, A. S¨onmez, C¸ . Genc, On an equivalence of topological vector space valued cone metric spaces and metric spaces, Appl. Math. Lett., 25 (2012), 429–433
-
[19]
W.-S. Du, A note on cone metric fixed point theory and its equivalence, Nonlinear Anal., 72 (2010), 2259–2261
-
[20]
W.-S. Du, E. Karapınar, A note on cone b-metric and its related results: generalizations or equivalence?, Fixed Point Theory Appl., 2013 (2013), 7 pages
-
[21]
E. El-Shobaky, S. M. Ali, M. S. Ali, Generalization of Banach contraction principle in two directions, J. Math. Stat., 3 (2007), 112–115
-
[22]
Y. Feng, W. Mao, The equivalence of cone metric spaces and metric spaces, Fixed Point Theory, 11 (2010), 259–263
-
[23]
D. J. Guo, V. Lakshmikantham, Coupled fixed points of nonlinear operators with applications, Nonlinear Anal., 11 (1987), 623–632
-
[24]
H. Huang, G. Deng, S. Radenovi´, Some topological properties and fixed point results in cone metric spaces over Banach algebras, Positivity, 23 (2019), 21–34
-
[25]
H. Huang, Z. Kadelburg, S. Radenovi´, A note on some recent results about multivalued mappings in tvs-cone metric spaces, J. Adv. Math. Stud., 9 (2016), 330–337
-
[26]
H. Huang, S. Radenovi´, Some fixed point results of generalized Lipschitz mappings on cone b-metric spaces over Banach algebras, J. Comput. Anal. Appl., 20 (2016), 566–583
-
[27]
H. Huang, S. Xu, Fixed point theorems of contractive mappings in cone b-metric spaces and applications, Fixed Point Theory Appl., 2013 (2013), 10 pages
-
[28]
L.-G. Huang, X. Zhang, Cone metric spaces and fixed point theorems of contractive mappings, J. Math. Anal. Appl., 332 (2007), 1468–1476
-
[29]
S. Jankovi´c, Z. Kadelburg, S. Radenovi´c, On cone metric spaces: A survey, Nonlinear Anal., 74 (2011), 2591–2601
-
[30]
S. Jiang, Z. Li, Extensions of Banach contraction principle to partial cone metric spaces over a non-normal solid cone, Fixed Point Theory Appl., 2013 (2013), 9 pages
-
[31]
Z. Kadelburg, S. Radenovi´, A note on various types of cones and fixed point results in cone metric spaces, Asian J. Math. Appl., 2013 (2013), 7 pages
-
[32]
Z. Kadelburg, S. Radenovi´c, V. Rakoˇcevi´, A note on equivalence of some metric and cone metric fixed point results, Appl. Math. Lett., 24 (2011), 370–374
-
[33]
M. A. Krasnosel Alski, P. P. Zabreiko, Geometrical Methods in Nonlinear Analysis, Springer-Verlag, Berlin (1984)
-
[34]
P. Kumam, N. V. Dung, V. T. L. Hang, Some equivalences between cone b-metric spaces and b-metric spaces, Abstr. Appl. Anal., 2013 (2013), 8 pages
-
[35]
Z. Li, S. Jiang, Common fixed point theorems of contractions in partial cone metric spaces over non-normal cones, Abstr. Appl. Anal., 2014 (2014), 8 pages
-
[36]
H. Liu, S. Xu, Cone metric spaces with Banach algebras and fixed point theorems of generalized Lipschitz mappings, Fixed Point Theory Appl., 2013 (2013), 10 pages
-
[37]
N. V. Luong, N. X. Thuan, K. P. R. Rao, Remarks on coupled fixed point theorems in cone metric spaces, Mat. Vesnik, 65 (2013), 122–136
-
[38]
S. G. Matthews, Partial metric topology, In: Proc. 8th Summer Conference on General Topology and Applications, New York Acad. Sci., New York, 728 (1994), 183–197
-
[39]
S. Moshokoa, On partial metric spaces and partial cone metric spaces, Hacet. J. Math. Stat., 46 (2017), 1069–1075
-
[40]
H. K. Nashine, Z. Kadelburg, S. Radenovi´, Coupled common fixed point theorems for w-compatible mappings in ordered cone metric spaceses, Appl. Math. Comput., 218 (2012), 5422–5432
-
[41]
S. Rezapour, R. Hamlbarani, Some notes on the paper: “Cone metric spaces and fixed point theorems of contractive mappings”, J. Math. Anal. Appl., 345 (2008), 719–724
-
[42]
W. Rudin, Functional analysis, McGraw-Hill, Inc., New York (1991)
-
[43]
F. Sabetghadam, H. P. Masiha, A. H. Sanatpour, Some Coupled Fixed Point Theorems in Cone Metric Spaces, Fixed Point Theory Appl., 2009 (2009), 8 pages
-
[44]
N. Sharma, Fixed point theorem in cone B metric spaces using contractive mappings, Glob. J. Pure Appl. Math., 13 (2017), 2997–3004
-
[45]
W. Shatanawi, Partially Ordered Cone Metric Spaces and Coupled Fixed Point Results, Comput. Math. Appl., 60 (2010), 2508–2515
-
[46]
L. Shi, S. Xu, Common fixed point theorems for two weakly compatible self-mappings in cone b-metric spaces, Fixed Point Theory Appl., 2013 (2013), 11 pages
-
[47]
J. S. Vandergraft, Newton method for convex operators in partially ordered spaces, SIAM J. Numer. Anal., 4 (1967), 406–432
-
[48]
S. Xu, S. Radenovi´c, Fixed point theorems of generalized Lipschitz mappings on cone metric spaces over Banach algebras without assumption of normality, Fixed Point Theory Appl., 2014 (2014), 12 pages
-
[49]
P. P. Zabrejko, K-metric and K-normed linear spaces: survey, Collect. Math., 48 (1997), 825–859
