For a complete extended b-metric space with continuous mapping satisfying the rational type contractive condition, a distinctive common fixed point theorem is established. Our outcome is the extension of several results available in the literature, from metric space to extended b-metric space. In specific, Dass and Gupta[Indian J. Pure Appl. Math. 6, 1455–1458 (1975)], Jaggi[Indian J. Pure Appl. Math. 8, 223–230 (1977)], Alqahtani et.al.[J. Inequal. Appl. Paper No. 220, 11 pp (2019)] and even the well-known Banach contraction mapping theory are extracted. A proper example is also given in sustenance of it.
REFERENCES
1.
B.
Alqahtani
; A.
Fulga
, E.
Karapınar
and V.
Rakôcevíc
, “Contractions with rational inequalities in the extended b-metric space
,” J. Inequal. Appl. Paper No. 220
, 11
pages (2019
).2.
B. K.
Dass
, S.
Gupta
, “An extension of Banach contraction principle through rational expressions
,” Indian J. Pure Appl. Math.
6
, 1455
–1458
(1975
).3.
D.S.
Jaggi
, “Some unique fixed point theorems
,” Indian J. Pure Appl. Math.
8
, 223
–230
(1977
).4.
I.A.
Bakhtin
, “The contraction principle in quasimetric spaces
,” Funct. Anal.
30
, 26
–37
(1989
).5.
S.
Czerwik
, “Contraction mappings in b-metric spaces
,” Acta Math. Inform., Univ. Ostrav.
, 1
, 5
–11
(1993
).6.
S.
Czerwik
, “Nonlinear set-valued contraction mappings in b-metric spaces
,” Atti Semin. Mat. Fis. Univ. Modena
46
(2
), 263
–276
(1998
).7.
T.
Kamran
, M.
Samreen
, O.U.
Ain
, “A generalization of b-metric space and some fixed point theorems
,” Mathematics
5
, 19
(2017
).
This content is only available via PDF.
© 2022 Author(s).
2022
Author(s)
You do not currently have access to this content.
