Existence fixed point in convex extended \(s\)-metric spaces with applications
Authors
Q. H. Alqifiary
- Department of Mathematics, College of Science, University of Al-Qadisiyah, Al-Diwaniya, Iraq.
C. Park
- Research Institute for Natural Sciences, Hanyang University, Seoul, 04763, Korea.
Abstract
In this paper, we introduce the definition of a convex extended \(s\)-metric space and establish the existence of fixed points for some contraction mappings in convex extended \(s\)-metric spaces. Additionally, we provide several examples to validate our findings. Furthermore, we apply the main results to approximate solutions of the Fredholm integral equation.
Share and Cite
ISRP Style
Q. H. Alqifiary, C. Park, Existence fixed point in convex extended \(s\)-metric spaces with applications, Journal of Nonlinear Sciences and Applications, 17 (2024), no. 3, 115--122
AMA Style
Alqifiary Q. H. , Park C., Existence fixed point in convex extended \(s\)-metric spaces with applications. J. Nonlinear Sci. Appl. (2024); 17(3):115--122
Chicago/Turabian Style
Alqifiary, Q. H. , Park, C.. "Existence fixed point in convex extended \(s\)-metric spaces with applications." Journal of Nonlinear Sciences and Applications, 17, no. 3 (2024): 115--122
Keywords
- Extended \(s\)-metric space
- convex structure
- convex extended \(s\)-metric space
- fixed point
- Fredholm integral equation
MSC
References
-
[1]
M. U. Ali, T. Kamran, M. Postolache, Solution of Volterra integral inclusion in b-metric spaces via new fixed point theorem, Nonlinear Anal. Model. Control, 22 (2017), 17–30
-
[2]
H. Aydi, N. Bilgili, E. Karapınar, Common fixed point results from quasi-metric spaces to G-metric spaces, J. Egyptian Math. Soc., 23 (2015), 356–361
-
[3]
I. A. Bakhtin, The contraction mapping principle in almost metric spaces, Funct. Anal., Gos. Ped. Inst. Unianowsk, 30 (1989), 26–37
-
[4]
I. Beg, A. Azam, Fixed point on starshaped subset of convex metric spaces, Indian J. Pure Appl. Math., 18 (1987), 594–596
-
[5]
I. Beg, N. Shahzad, M. Iqbal, Fixed point theorems and best approximation in convex metric space, Approx. Theory Appl., 8 (1992), 97–105
-
[6]
M. Bota, A. Moln´ar, C. Varga, On Ekeland’s variational principle in b-metric spaces, Fixed Point Theory, 12 (2012), 21–28
-
[7]
S. Czerwik, Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis, 1 (1993), 5–11
-
[8]
X. P. Ding, Iteration processes for nonlinear mappings in convex metric spaces, J. Math. Anal. Appl., 132 (1988), 114–122
-
[9]
N. V. Dung, V. T. L. Hang, Remarks on partial b-metric spaces and fixed point theorems, Mat. Vesnik, 69 (2017), 231–240
-
[10]
A. Felhi, S. Sahmim, H. Aydi, Ulam-Hyers stability and well-posedness of fixed point problems for --contractions on quasi b-metric spaces, Fixed Point Theory Appl., 2016 (2016), 20 pages
-
[11]
K. Goebel, W. A Kirk, Iteration processes for nonexpansive mappings, In: Topological methods in nonlinear functional analysis (Toronto, Ont., 1982), Amer. Math. Soc., Providence, RI, 21 (1983), 115–123
-
[12]
M. D. Guay, K. L. Singh, J. H. M. Whitfield, Fixed point Theorems for nonexpansive mappings in convex metric spaces, In: Nonlinear analysis and applications (St. Johns, Nfld.,1981), Dekker, New York, 80 (1982), 179–189
-
[13]
M. Imdad, M. Asim, R. Gubran, Common fixed point theorems for g-generalized contractive mappings in b-metric spaces, Indian J. Math., 60 (2018), 85–105
-
[14]
A. Kari, A. Al-Rawashdeh, New fixed point theorems for -!-contraction on (, )-generalized metric spaces, J. Funct. Space, 2023 (2023), 14 pages
-
[15]
A. Kari, H. A. Hammad, A. Baiz, M. Jamal, Best proximity point of generalized (F - ) proximal non-self contractions in generalized metric spaces, Appl. Math. Inf. Sci., 16 (2022), 853–861
-
[16]
A. Kari, M. Rossafi, J. R. Lee, FIXED POINT THEOREMS IN QUASI-METRIC SPACES, Nonlinear Funct. Anal. Appl., 28 (2023), 311–335
-
[17]
T. Kamran, M. Samreen, Q. UL Ain, A generalization of b-metric space and some fixed point theorems, Mathematics, 5 (2017), 7 pages
-
[18]
T. Kamran, M. Postolache, M. U. Ali, Q. Kiran, Feng and Liu type F-contraction in b-metric spaces with an application to integral equations, J. Math. Anal., 7 (2016), 18–27
-
[19]
W. A. Kirk, Krasnoselski˘ı’s iteration process in hyperbolic space, Numer. Funct. Anal. Optim., 4 (1981/82), 371–381
-
[20]
A. Kumar, S. Rathee, Some common fixed point and invariant approximation results for nonexpansive mappings in convex metric space, Fixed Point Theory Appl., 2014 (2014), 14 pages
-
[21]
A. Kumar, A. Tas, Note on common fixed point theorems in convex metric spaces, Axioms, 10 (2021), 1–7
-
[22]
M. Rossafi, A. Kari, New fixed point theorems for ( , F)-contraction on rectangular b-metric spaces, Afr. Mat., 34 (2023), 26 pages
-
[23]
M. Rossafi, A. Kari, C. Park, J. R. Lee, New fixed point theorems for - - contraction on b-metric spaces, J. Math. Comput. Sci., 29 (2023), 12–27
-
[24]
Z. Mustafa, J. R. Roshan, V. Parvaneh, Z. Kadelburg, Some common fixed point results in ordered partial b-metric spaces, J. Inequal. Appl., 2013 (2013), 26 pages
-
[25]
M. Samreen, T. Kamran, M. Postolache, Extended b-metric space, extended b-comparison function and nonlinear contractions, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys., 80 (2018), 21–28
-
[26]
W. Takahashi, A convexity in metric space and nonexpansive mappings. I, Kodai Math. Sem. Rep., 22 (1970), 142–149
