SOME FIXED POINT RESULTS FOR CONVEX CONTRACTION MAPPINGS ON F-METRIC SPACES
Abstract
In this paper, we establish some fixed point theorems for convex contraction mappings in F-metric spaces. Also, we introduce the concept of (\alpha,\beta)-convex contraction mapping in F-metric spaces and give some fixed point results for such contractions. Moreover, some examples are given to support our theoretical results.
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S. P. Acharya: Some results on fixed points in uniform spaces. Yokohama Math.
J. 22 (1974), 105–116.
C. D. Alecsa: Some fixed point results regarding convex contractions of Presi´ c
type. J. Fixed Point Theory Appl. 20(1) (2018), Art. 7, 19 pp.
M. A. Alghamdi, S. H. Alnafei, S. Radenovi´ c and N. Shahzad: Fixed point
theorems for convex contraction mappings on cone metric spaces. Math. Comput. Modelling 54 (2011), no. 9-10, 2020–2026.
I. A. Bakhtin: The contraction mapping principle in almost metric space. Func-
tional analysis, (Russian), Ul´ yanovsk. Gos. Ped. Inst., Ul´ yanovsk, (1989), 26–37.
R. K. Bisht and N. Hussain: A note on convex contraction mappings and dis-
continuity at fixed point. J. Math. Anal. 8(4), (2017), 90–96.
L. B. Ciri´ c: Some Recent Results in Metrical Fixed Point Theory. Faculty of
Mechanical Engineering, University of Belgrade, Belgrade, 2003.
D. D. Doli´ canin and B. B. Mohsin: Some new fixed point results for convex
contractions in b-metric spaces. Univ. Thought Pub. Nat. Sci. 9(1), (2019), 67–71.
K. S. Eke, V. O. Olisama and S. A. Bishop: Some fixed point theorems for
convex contractive mappings in complete metric spaces with applications. Cogent
Math. Stat. 6(1) (2019), Art. ID 1655870, 10 pp.
H. Faraji, K. Nourouzi and D. O’Regan: A fixed point theorem in uniform
spaces generated by a family of b-pseudometrics. Fixed Point Theory 20 (1),
(2019), 177–183.
H. Faraji, D. Savi´ c, and S. Radenovi´ c: Fixed point theorems for Geraghty
contraction type mappings in b-metric spaces and applications. Axioms 8 (34),
(2019).
F. Georgescu: IFSs consisting of generalized convex contractions. An. S ¸tiint ¸.
Univ. ”Ovidius” Constant ¸a Ser. Mat. 25 (1) (2017), 77–86.
R. George, A. H. Nabwey, R. Ramaswamy, S. Radenovi´ c and K. P.
Reshma: Rectangular cone b-metric spaces over Banach algebra and contraction
principle. Fixed Point Theory Appl. 2017, Paper No. 14, 15 pp.
A. Hussain and T. Kanwal: Existence and uniqueness for a neutral differential
problem with unbounded delay via fixed point results. Trans. A. Razmadze Math.
Inst. 172 (3), (2018),part B, 481–490.
V. I. Istratescu: Some fixed point theorems for convex contraction mappings and
mappings with convex diminishing diameters. I. Ann. Mat. Pura Appl. 130(4),
(1982), 89–104.
V. I. Istratescu: Some fixed point theorems for convex contraction mappings and
mappings with convex diminishing diameters. II. Ann. Mat. Pura Appl. 134(4),
(1983), 327–362.
W. Kirk and N. Shahzad: Fixed Point Theory in Distances Spaces. Springer:
Berlin, Germany, 2014.
M. Jleli and B. Samet: On a new generalization of metric spaces. J. Fixed
Point Theory Appl. 20(30), (2018), Art. 128, 20 pp.
S.G. Matthews: Partial metric topology. Research Report 212, Dept. of Com-
puter Science, University of Warwick, 1992.
M. A. Miandaragh, M. Postolache and S. Rezapour: Approximate fixed
points of generalized convex contractions. Fixed Point Theory Appl. 2013,
:255, 8 pp.
Z. D. Mitrovi´ c, H. Aydi, N. Hussain and A. Mukheimer: Reich, Jungck,
and Berinde common fixed point results on F-metric spaces and an application. Mathematics (2019), 7, 387.
Z. D. Mitrovi´ c, H. Aydi, N. Mlaiki, M. Gardaˇ sevi´ c-Filipovi´ c, K. Kuki´ c
and S. Radenovi´ c: Some New Observations and Results for Convex Contractions of Isatratescu’s Type. Symmetry 2019, 11, 1457, doi:10.3390/sym11121457.
DOI: https://doi.org/10.22190/FUMI2004939F
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