Application of a-b-FG-Khan contractions to an initial value problem in b-metric spaces
*Gehad M. Abd-ElhamedCorresponding authorgehadmahfood@gmail.comAffiliation 1Department of MathematicsCollege of Science and Humanities StudiesPrince Sattam Bin Abdulaziz UniversityAlkharj, 11942, Saudi ArabiaAffiliation 2Department of MathematicsCollege of GirlsAin Shams UniversityCairo, EgyptView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 09 Apr 2025
- Published Online:
- 02 Feb 2026
- Article type:
- Research Article
- Language:
- EN
- Article no.:
- JIM-2399
- Pages:
- 465–476
Abstract
Keywords
Subject Classifications
References
[1] M. Abbas, B. Ali and S. Romaguera, “Fixed and periodic points of generalized contractions in metric spaces”, Fixed Point Theory Appl, 2013, 243 (2013): https://doi.org/10.1186/1687-1812-2013-243.
[2] G. M. Abd-Elhamed, “Fixed point results for (α,β)-implicit contractions in two generalized b-metric spaces”, J. Nonlinear Sci. Appl., vol. 14, pp. 39 – 47 (2021): https://doi.org/10.22436/jnsa.014.01.05.
[3] G. M. Abd-Elhamed, “Fixed point theorems for functions satisfying implicit relations in generalized b-metric spaces”, International Journal of Mathematics and Computer Science, vol.15, no. 1, pp. 1-10(2020): http://ijmcs.future-in-tech.net.
[4] G. M. Abd-Elhamed and A. A. Azzam, “Applications of different types of Khan contractions in convex b-metric spaces”, J. Math. Computer Sci., vol. 38, pp. 417–429(2025): https://doi.org/10.22436/jmcs.038.04.01.
[5] G. M. Abd-Elhamed and A. A. Azzam , “Fixed Points in generalized alfa-Beta -FG contractions in b-metric spaces”, Journal of Interdisciplinary Mathematics, vol. 28, no. 2, pp. 677-689(2025), doi: 10.47974/JIM-2126.
[6] I. A. Bakhtin, “The contraction principle in quasimetric spaces”, Funk An Ulianowsk Gos Ped Inst, vol. 30, pp. 26–37(1989).
[7] R. Batra, R. Gupta, and P. Sahni, “Some results related to fixed points of F-G-contractions on metric spaces equipped with w-distance”, Journal of Interdisciplinary Mathematics, vol. 23, no. 2, pp. 413–423(2020): https://doi.org/10.1080/09720502.2020.1731954.
[8] S. Czerwik, “Contraction mappings in b-metric spaces”, Acta Math Inf Univ Ostrav, vol. 1, pp. 5–11(1993).
[9] S. Czerwik, “Nonlinear set-valued contraction mappings in b-metric spaces”, Atti Sem Mat Fis Univ Modena, vol. 46, pp.263–276(1998).
[10] S. H. Hadi and Z. S. Madhi, “Fixed-point theorems of FR-Ćirić-pata type in Fuzzy-Riesz I-Convex Metric Space (FRCMS)”, Journal of Interdisciplinary Mathematics, vol. 24, no. 8, pp. 2181–2193(2021): https://doi.org/10.1080/09720502.2020.1862956.
[11] N. Hussain, M. A. Kutbi and P. Salimi, “Fixed point theory in α-complete metric spaces with applications”, Abstract Appl Anal, pp.1-11 (2014), DOI: 10.1155/2014/280817.
[12] N. Hussain, P. Salimi and A. Latif, “Fixed point results for single and set-valued α-η-ψ contractive mappings”, Fixed Point Theory Appl, 2013, 212 (2013): https://doi.org/10.1186/1687-1812-2013-212.
[13] N. Hussain, D. Doric, Z. Kadelburg and S. Radenovic, “Generalized wardowski type fixed point theorems via α-admissible FG contractions in b-metric spaces”, Acta Mathematica Scientia, vol. 36, no. 5, pp. 1445–1456(2016): https://doi.org/10.1016/S0252-9602(16)30080-7.
[14] K. Karap nar, P. Kumam and P. Salimi, “ On α-ψ-Meir-Keeler contractive mappings”, Fixed Point Theory Appl, 2013, 94 (2013): https://doi.org/10.1186/1687-1812-2013-94.
[15] M. A. Khamsi and N. Hussain, “KKM mappings in metric type spaces”, Nonlinear Anal, vol. 73, no. 9, pp. 3123–3129(2010).
[16] A. Raturi and S. S. Chauhan, “New results in bipolar controlled b-dislocated metric space and its applications for solving fractional differential equations”, Journal of Interdisciplinary Mathematics, vol. 27, no. 8, pp. 1797-1830(2024): https://doi.org/10.47974/JIM-2043.
[17] P. Salimi, A. Latif and H. Hussain, “Modified α-ψ-contractive mappings with applications”, Fixed Point Theory Appl, 2013, 151 (2013): https://doi.org/10.1186/1687-1812-2013-151.
[18] B. Samet, C. Vetro and P. Vetro, “Fixed point theorem for α-ψ-contractive type mappings”, Nonlinear Anal, vol. 75, pp. 2154–2165(2012): https://doi.org/10.31801/cfsuasmas.424203.
[19] D. Wardowski , “Fixed points of a new type of contractive mappings in complete metric spaces”, Fixed Point Theory Appl, (2012): https://doi.org/10.1186/1687-1812-2012-94.
[20] D. Wardowski and N. Van Dung, “Fixed points of F-weak contractions on complete metric spaces”, Demonstratio Math, vol. 47, no. 1, 146–155(2014): https://doi.org/10.2478/dema-2014-0012.
[21] H. Piri and P. Kumam, “Some fixed point theorems concerning F-contraction in complete metric spaces”, Fixed Point Theory Appl, 2014, 210 (2014): https://doi.org/10.1186/1687-1812-2014-210.




