Journal of Mathematics and Applications
02/42, DOI: 10.7862/rf.2019.2
On Some Fixed Point Theorems for Expansive Mappings in Dislocated Cone Metric Spaces with Banach Algebras
Abba Auwalu, Evren Hinçal, Lakshmi Narayan Mishra
DOI: 10.7862/rf.2019.2
Abstract
In this paper, we introduced the notion of generalized expansive mappings in dislocated cone metric spaces with Banach algebras. Furthermore, we prove some fixed point theorems for generalized expansive mappings in dislocated cone metric spaces with Banach algebras without the assumption of normality of cones. Moreover, we give an example to elucidate our result. Our results are significant extension and generalizations of many recent results in the literature.
References
- C.T. Aage, J.N. Salunke, Some fixed point theorems for expansion onto mappings on cone metric spaces, Acta Mathematica Sinica (English series) 27 (6) (2011) 1101-1106.
- A. Auwalu, A note on some fixed point theorems for generalized expansive mappings in cone metric spaces over Banach algebras, AIP Conference Proc. 1997 (020004) (2018) 1-7.
- S. Chouhan, N. Malviya, A fixed point theorem for expansive type mappings in cone metric spaces, Int. Math. Forum 6 (18) (2011) 891-897.
- Deepmala, R.P. Agarwal, Existence and uniqueness of solutions for certain functional equations and system of functional equations arising in dynamic programming, An. St. Univ. Ovidius Constanta, Math. Series 24 (1) (2016) 3-28.
- Deepmala, A.K. Das, On solvability for certain functional equations arising in dynamic programming, Mathematics and Computing, Springer Proceedings in Mathematics and Statistics 139 (2015) 79-94.
- R. George, R. Rajagopalan, H.A. Nabwey, S. Radenović, Dislocated cone metric space over Banach algebras and α-quasi contraction mappings of Perov type, Fixed Point Theory Appl. (2017) 2017:24.
- H. Huang, S. Radenović, Common fixed point theorems of generalized Lipschitz mappings in cone metric spaces over Banach algebras, Appl. Math. Inf. Sci. 9 (6) (2015) 2983-2990.
- H. Huang, S. Radenović, Common fixed point theorems of generalized Lipschitz mappings in cone b-metric spaces over Banach algebras and applications, J. Nonlinear Sci. Appl. 8 (2015) 787-799.
- L.G. Huang, X. Zhang, Cone metric spaces and fixed point theorems for contractive mappings, J. Math. Anal. Appl. 332 (2) (2007) 1468-1476.
- X. Huang, C. Zhu, X. Wen, Fixed point theorems for expanding mappings in cone metric spaces, Math. Reports 14 (2) (2012) 141-148.
- B. Jiang, S. Xu, H. Huang, Z. Cai, Some fixed point theorems for generalized expansive mappings in cone metric spaces over Banach algebras, J. Comput. Anal. Appl. 21 (6) (2016) 1103-1114.
- Z. Kadelburg, S. Radenović, A note on various types of cones and fixed point results in cone metric spaces, Asian J. Math. Appl., Article ID ama0104 (2013) 7 pages.
- H. Liu, S. Xu, Cone metric spaces with Banach algebras and fixed point theorems of generalized Lipschitz mappings, Fixed Point Theory Appl. (2013) 2013:320.
- L.N. Mishra, M. Sen, On the concept of existence and local attractivity of solutions for some quadratic Volterra integral equation of fractional order, Appl. Math. Comput. 285 (2016) 174-183.
- L.N. Mishra, M. Sen, R.N. Mohapatra, On existence theorems for some generalized nonlinear functional-integral equations with applications, Filomat 31 (7) (2017) 2081-2091.
- V.N. Mishra, Some Problems on Approximations of Functions in Banach Spaces, Ph.D. Thesis, Indian Institute of Technology, Roorkee 247 667, Uttarakhand, India, 2016.
- P.P. Murthy, Rashmi, V.N. Mishra, Tripled coincidence point theorem for compatible maps in fuzzy metric spaces, Electronic Journal of Mathematical Analysis and Applications 4 (2) (2016) 96-106.
- W. Rudin, Functional Analysis, 2nd edition, McGraw-Hill, New York, 1991.
- S.Z. Wang, B.Y. Li, Z.M. Gao, K. Iseki, Some fixed point theorems for expansion mappings, Math. Japon. 29 (1984) 631-636.
- S. Xu, S. Radenović, Fixed point theorems of generalized Lipschitz mappings on cone metric spaces over Banach algebras without assumption of normality, Fixed Point Theory Appl. (2014) 2014:102.
About this Article
TITLE:
On Some Fixed Point Theorems for Expansive Mappings in Dislocated Cone Metric Spaces with Banach Algebras
AUTHORS:
Abba Auwalu (1)
Evren Hinçal (2)
Lakshmi Narayan Mishra (3)
AUTHORS AFFILIATIONS:
(1) Near East University, TURKEY
(2) Near East University, TURKEY
(3) Vellore Institute of Technology (VIT) University, INDIA
JOURNAL:
Journal of Mathematics and Applications
02/42
KEY WORDS AND PHRASES:
Dislocated cone metric space over Banach algebras; Expansive mapping; Fixed point; c-sequence.
FULL TEXT:
http://doi.prz.edu.pl/pl/pdf/jma/79
DOI:
10.7862/rf.2019.2
URL:
http://dx.doi.org/10.7862/rf.2019.2
RECEIVED:
2018-11-21
ACCEPTED:
2019-03-08
COPYRIGHT:
Oficyna Wydawnicza Politechniki Rzeszowskiej, al. Powstańców Warszawy 12, 35-959 Rzeszów