Geodesic
Existence fixed point in convex extended $s$-metric spaces with applications
Alqifiary, Q‎. ‎H‎. ‎1 ; Park, C.2
1 Department of Mathematics‎, ‎College of Science, ‎University of Al-Qadisiyah, ‎Al-Diwaniya, Iraq
2 Research Institute for Natural Sciences, ‎Hanyang University, Seoul, 04763, Korea
Journal of nonlinear sciences and its applications, Tome 17 (2024) no. 3, p. 115-122.

Voir la notice de l'article provenant de la source International Scientific Research Publications

‎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.‎
DOI : 10.22436/jnsa.017.03.01
Classification : 35B40, 74F05, 93D15, 47H10
Keywords: Extended \(s\)-metric space, convex structure, convex extended \(s\)-metric space, fixed point, Fredholm integral equation

Alqifiary, Q‎. ‎H‎. ‎ 1 ; Park, C. 2

1 Department of Mathematics‎, ‎College of Science, ‎University of Al-Qadisiyah, ‎Al-Diwaniya, Iraq
2 Research Institute for Natural Sciences, ‎Hanyang University, Seoul, 04763, Korea 
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Alqifiary, Q‎. ‎H‎. ‎; Park, C. Existence  fixed point in convex extended \(s\)-metric spaces with applications. Journal of nonlinear sciences and its applications, Tome 17 (2024) no. 3, p. 115-122. doi : 10.22436/jnsa.017.03.01. http://geodesic.mathdoc.fr/articles/10.22436/jnsa.017.03.01/

[1] Ali, M. U.; Kamran, T.; Postolache, M. Solution of Volterra integral inclusion in b-metric spaces via new fixed point theorem, Nonlinear Anal. Model. Control, Volume 22 (2017), pp. 17-30 | DOI | Zbl

[2] Aydi, H.; Bilgili, N.; Karapınar, E. Common fixed point results from quasi-metric spaces to G-metric spaces, J. Egyptian Math. Soc., Volume 23 (2015), pp. 356-361 | Zbl | DOI

[3] Bakhtin, I. A. The contraction mapping principle in almost metric spaces, Funct. Anal., Gos. Ped. Inst. Unianowsk, Volume 30 (1989), pp. 26-37 | Zbl

[4] Beg, I.; Azam, A. Fixed point on starshaped subset of convex metric spaces, Indian J. Pure Appl. Math., Volume 18 (1987), pp. 594-596

[5] Beg, I.; Shahzad, N.; Iqbal, M. Fixed point theorems and best approximation in convex metric space, Approx. Theory Appl., Volume 8 (1992), pp. 97-105

[6] Bota, M.; Moln´ar, A.; Varga, C. On Ekeland’s variational principle in b-metric spaces, Fixed Point Theory, Volume 12 (2012), pp. 21-28 | Zbl

[7] Czerwik, S. Contraction mappings in b-metric spaces, Acta Math. Inform. Univ. Ostraviensis, Volume 1 (1993), pp. 5-11

[8] Ding, X. P. Iteration processes for nonlinear mappings in convex metric spaces, J. Math. Anal. Appl., Volume 132 (1988), pp. 114-122 | Zbl | DOI

[9] Dung, N. V.; Hang, V. T. L. Remarks on partial b-metric spaces and fixed point theorems, Mat. Vesnik, Volume 69 (2017), pp. 231-240 | Zbl

[10] Felhi, A.; Sahmim, S.; Aydi, H. Ulam-Hyers stability and well-posedness of fixed point problems for - -contractions on quasi b-metric spaces, Fixed Point Theory Appl., Volume 2016 (2016), pp. 1-20 | Zbl | DOI

[11] Goebel, K.; Kirk, W. A Iteration processes for nonexpansive mappings, In: Topological methods in nonlinear functional analysis (Toronto, Ont., 1982), Amer. Math. Soc., Providence, RI, Volume 21 (1983), pp. 115-123 | DOI

[12] Guay, M. D.; Singh, K. L.; Whitfield, J. H. M. Fixed point Theorems for nonexpansive mappings in convex metric spaces, In: Nonlinear analysis and applications (St. Johns, Nfld.,1981), Dekker, New York, Volume 80 (1982), pp. 179-189

[13] Imdad, M.; Asim, M.; Gubran, R. Common fixed point theorems for g-generalized contractive mappings in b-metric spaces, Indian J. Math., Volume 60 (2018), pp. 85-105 | Zbl

[14] Kari, A.; Al-Rawashdeh, A. New fixed point theorems for -!-contraction on ( , )-generalized metric spaces, J. Funct. Space, Volume 2023 (2023), pp. 1-14 | Zbl | DOI

[15] Kari, A.; Hammad, H. A.; Baiz, A.; Jamal, M. Best proximity point of generalized (F - ) proximal non-self contractions in generalized metric spaces, Appl. Math. Inf. Sci., Volume 16 (2022), pp. 853-861

[16] Kari, A.; Rossafi, M.; Lee, J. R. FIXED POINT THEOREMS IN QUASI-METRIC SPACES, Nonlinear Funct. Anal. Appl., Volume 28 (2023), pp. 311-335 | Zbl

[17] Kamran, T.; Samreen, M.; Ain, Q. UL A generalization of b-metric space and some fixed point theorems, Mathematics, Volume 5 (2017), pp. 1-7 | Zbl | DOI

[18] Kamran, T.; Postolache, M.; Ali, M. U.; Kiran, Q. Feng and Liu type F-contraction in b-metric spaces with an application to integral equations, J. Math. Anal., Volume 7 (2016), pp. 18-27 | Zbl

[19] Kirk, W. A. Krasnoselski˘ı’s iteration process in hyperbolic space, Numer. Funct. Anal. Optim., Volume 4 (1981/82), pp. 371-381 | Zbl | DOI

[20] Kumar, A.; Rathee, S. Some common fixed point and invariant approximation results for nonexpansive mappings in convex metric space, Fixed Point Theory Appl., Volume 2014 (2014), pp. 1-14 | DOI | Zbl

[21] Kumar, A.; Tas, A. Note on common fixed point theorems in convex metric spaces, Axioms, Volume 10 (2021), pp. 1-7 | DOI

[22] Rossafi, M.; Kari, A. New fixed point theorems for ( , F)-contraction on rectangular b-metric spaces, Afr. Mat., Volume 34 (2023), pp. 1-26 | DOI | Zbl

[23] Rossafi, M.; Kari, A.; Park, C.; Lee, J. R. New fixed point theorems for - - contraction on b-metric spaces, J. Math. Comput. Sci., Volume 29 (2023), pp. 12-27

[24] Mustafa, Z.; Roshan, J. R.; Parvaneh, V.; Kadelburg, Z. Some common fixed point results in ordered partial b-metric spaces, J. Inequal. Appl., Volume 2013 (2013), pp. 1-26 | DOI | Zbl

[25] Samreen, M.; Kamran, T.; Postolache, M. Extended b-metric space, extended b-comparison function and nonlinear contractions, Politehn. Univ. Bucharest Sci. Bull. Ser. A Appl. Math. Phys., Volume 80 (2018), pp. 21-28 | Zbl

[26] Takahashi, W. A convexity in metric space and nonexpansive mappings. I, Kodai Math. Sem. Rep., Volume 22 (1970), pp. 142-149 | Zbl

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