The purpose of this note is to prove an existence theorem of fixed point for θ-type contraction in the setting of M- complete M-metric spaces. The results presented in the paper improve and extend the corresponding results in Banach [6], Asadi at. al. [5], Jleli and Samet [12]. We give an example to illustrate this fact.
REFERENCES
1.
J.
Ahmad
, A. E.
Al-Mazrooei
, Y. J.
Cho
and Y. O.
Yang
, “Fixed point results for generalized θ-contractions
,” J. Nonlinear Sci. Appl.
10
, (2017
).2.
I.
Altun
, H. A.
Hançer
and G.
Mınak
, “On a general class of weakly Picard operators
,” Miskolc Mathematical Notes.
16
, 25
–32
(2015
).3.
I.
Altun
and G.
Minak
, “On fixed point theorems for multivalued mappings of Feng-Liu type
,” Bulletin of the Korean Mathematical Society.
52
, (2015
).4.
I.
Altun
, H.
Sahin
, and D.
Turkoglu
, “Fixed point results for multivalued mappings of Feng-Liu type on M-metric spaces
,” J. Nonlinear Funct. Anal.
2018
, (2018
).5.
M.
Asadi
, E.
Karapınar
and P.
Salimi
, “New extension of p-metric spaces with some fixed-point results on M-metric spaces
,” Journal of Inequalities and Applications.
1
, (2014
).6.
S.
Banach
, “Sur les operations dans les ensembles abstraits et leur applications aux equations integrales
,” Fundam. Math.
3
, (1922
).7.
G.
Durmaz
and I.
Altun
, “A new perspective for multivalued weakly picard operators
,” Publications de l’Institut Mathematique.
101
, (2017
).8.
G.
Durmaz
and I.
Altun
, “On Nonlinear Set-Valued θ-Contractions
,” Bulletin of the Malaysian Mathematical Sciences Society.
43
, (2020
).9.
H. A.
Hançer
, G.
Mınak
and I.
Altun
,” On a broad category of multivalued weakly Picard operators,” Fixed Point Theory.
18
, (2017
).10.
N.
Hussain
, V.
Parvaneh
, B.
Samet
and C.
Vetro
, “Some fixed point theorems for generalized contractive mappings in complete metric spaces
,” Fixed Point Theory and Applications.
1
, (2015
).11.
M.
Jleli
, E.
Karapınar
and B.
Samet
, “Further generalizations of the Banach contraction principle
,” Journal of Inequalities and Applications.
1
, (2014
).12.
M.
Jleli
and B.
Samet
, “A new generalization of the Banach contraction principle
,” Journal of inequalities and applications.
1
, (2014
).13.
X. D.
Liu
, S. S.
Chang
, Y.
Xiao
and L. C.
Zhao
, “Existence of fixed points for θ-type contraction and θ-type Suzuki contraction in complete metric spaces
,” Fixed Point Theory and Applications.
1
, (2016
).14.
H.
Sahin
, I.
Altun
and D.
Turkoglu
, “Two fixed point results for multivalued F-contractions on M-metric spaces
,” Revista de la Real Academia de Ciencias Exactas, Fisicas y Naturales. Serie A. Matematicas.
113
, (2019
).15.
H.
Sahin
, I.
Altun
and D.
Turkoglu
, “Fixed Point Results for Mixed Multivalued Mappings of Feng-Liu Type on M b-Metric Spaces,” Mathematical Methods in Engineering
(pp. 67
–80
). Springer
, (2019
).
This content is only available via PDF.
© 2022 Author(s).
2022
Author(s)
You do not currently have access to this content.
