Some Fixed Point of Hardy-Rogers Contraction in Generalized Complex Valued Metric Spaces
In this work, we defined the generalized complex valued metric space for some partial order relation and give some example. Then we study and established a fixed point theorem for general Hardy-Rogers contraction. The results extend and improve some results of Elkouch and Marhrani .
A. Azam, F. Brain and M. Khan, Common fixed point theorems in complex valued metric space, Numer.Funct.Anal. Optim. 32(3) (2011), 243 – 253.
S. Banach, Sur operations dams les ensembles abstraits et leur application aus equation integral, Fund. Math. 3(1922), 133 – 181.
V. Berinde, Iterative Approximation of fixed points, Lecture Notes in Mathematics, 2nd edition, Springer, Berlin (2007), DOI: 10.1007/978-3-540-72234-2.
S. K. Datta and S. Ali, A common fixed point theorems under contractive condition in complex valued metric space, International Journal of Advanced Scientific and Technical Research 6(2) (2012), 467 – 475.
Y. Elkouch and E. M. Morhrani, On some fixed point theorem in generalized metric space, Fixed Point Theory Applications 23(2017), 17 pages, DOI: 10.1186/s13663-017-0617-9.
G. D. Hardy and T. D. Roger, A generalization of a fixed point theorem of Riech, Can. Math. Bull. 16 (1973), 201 – 206.
M. Jleli and B. Samet, A generalized metric space and related fixed point theorems, Fixed Point Theory Appl. 2015 (2015):65, pages 1 – 14, DOI: 10.1186/s13663-015-0312-7.
R. Kannan, Some results on fixed points, Bull. Calcutta Math. Soc. 60 (1968), 71 – 76.
K. Khammahawong and P. Kumam, A best proximity point theorem for Roger–Hardy type generalized F-contractive mappings in complete metric spaces with some examples, Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A. Matemáticas 112 (2018), 1503 – 1519, DOI: 10.1007/s13398-017-0440-5.
P. Saipara, P. Kumam and Y. J. Cho, Random fixed point theorems for Hardy-Rogers self-random operators with applications to random integral equations, An International Journal of Probability and Stochastic Processes 90(2) (2018), 297 – 311, DOI: 10.1080/17442508.2017.1346655.
- There are currently no refbacks.
eISSN 0975-8607; pISSN 0976-5905