Fixed Point Theorems for Almost $\alpha$-$\psi$-Contractive Mappings in F-metric Spaces

Year 2024, Volume: 7 Issue: 4, 203 - 211, 31.12.2024

Canan Acar , Vildan Öztürk

https://doi.org/10.33401/fujma.1400093

Abstract

In this paper, we introduce an almost $\alpha$-$\psi$-contraction and a rational type $\alpha$-$\psi$-contraction for $\alpha$-admissible mappings in complete $F$-metric spaces which were introduced as a generalization of metric spaces. We prove the existence of a fixed point for these type contractions.

Keywords

Almost contraction, $\alpha$-Admissible mapping, Fixed point, $F$-Metric

References

• [1] M. Jleli and B. Samet, On a new generalization of metric spaces, J. Fixed Point Theory Appl., 20(3) (2018), 128, 1-20. $ \href{https://doi.org/10.1007/s11784-018-0606-6}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85051068232&origin=resultslist&sort=plf-f&src=s&sid=d29218f01edc11e7bf35362dd2f7c5e9&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22On+a+new+generalization+of+metric+spaces%22%29&sl=78&sessionSearchId=d29218f01edc11e7bf35362dd2f7c5e9&relpos=4}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000440495200002}{\mbox{[Web of Science]}} $
• [2] A. Hussain and T. Kanwal, Existence and uniqueness for a neutral differential problem with unbounded delay via fixed point results, Trans. A. Razmadze Math. Institute, 172(3) (2018), 481-490. $ \href{https://doi.org/10.1016/j.trmi.2018.08.006}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85056897331&origin=resultslist&sort=plf-f&src=s&sid=d29218f01edc11e7bf35362dd2f7c5e9&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Existence+and+uniqueness+for+a+neutral+differential+problem+with+unbounded+delay+via+fixed+point+results%22%29&sl=78&sessionSearchId=d29218f01edc11e7bf35362dd2f7c5e9&relpos=1}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000450363200001}{\mbox{[Web of Science]}} $
• [3] Z.D. Mitrovic, H. Aydi, N. Hussain and A. Mukheimer, Reich, Jungck, and Berinde common fixed point results on F-metric spaces and an application, Mathematics, 7(5) (2019), 387, 1-10. $ \href{https://doi.org/10.3390/math7050387}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85073696170&origin=resultslist&sort=plf-f&src=s&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Reich%2C+Jungck%2C+and+Berinde+common+fixed+point+results+on+F-metric+spaces+and+an+application%22%29&sessionSearchId=502a560a04d6610739b2929b83131935&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000472664400009}{\mbox{[Web of Science]}} $
• [4] D. Lateefa and J. Ahmad, Dass and Gupta’s fixed point theorem in F-metric spaces, J. Nonlinear Sci. Appl., 12(6) (2019), 405-411. $ \href{http://dx.doi.org/10.22436/jnsa.012.06.06}{\mbox{[CrossRef]}} $
• [5] F. Jahangir, P. Haghmaram and K. Nourouzi, A note on F-metric spaces, J. Fixed Point Theory Appl., 23(1) (2021), 2, 1-14. $ \href{https://doi.org/10.1007/s11784-020-00836-y}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85095937448&origin=resultslist&sort=plf-f&src=s&sid=d29218f01edc11e7bf35362dd2f7c5e9&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22A+note+on+F-metric+spaces%22%29&sl=78&sessionSearchId=d29218f01edc11e7bf35362dd2f7c5e9&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000594177900002}{\mbox{[Web of Science]}} $
• [6] İ. Altun and A. Erduran, Two fixed point results on F-metric spaces, Topol. Algebra Appl.,10(1) (2022), 61-67. $ \href{https://doi.org/10.1515/taa-2022-0114}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85134508709&origin=resultslist&sort=plf-f&src=s&sid=d29218f01edc11e7bf35362dd2f7c5e9&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Two+fixed+point+results+on+F-metric+spaces%22%29&sl=78&sessionSearchId=d29218f01edc11e7bf35362dd2f7c5e9&relpos=0}{\mbox{[Scopus]}} $
• [7] V. Özturk, Some results for Ciric Presic type contractions in F-metric spaces, Symmetry, 15(8) (2023), 1521, 1-12. $ \href{https://doi.org/10.3390/sym15081521}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85168891281&origin=resultslist&sort=plf-f&src=s&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Some+results+for+%C4%86iri%C4%87+Pre%C5%A1i%C4%87+type+contractions+in+F-metric+spaces%22%29&sessionSearchId=502a560a04d6610739b2929b83131935&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:001056057800001}{\mbox{[Web of Science]}} $
• [8] D. Lateefa, Best proximity point in F-metric spaces with applications, Demonstr. Math., 56(1) (2023), 20220191, 1-14. $\href{http://dx.doi.org/10.1515/dema-2022-0191}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85153952938&origin=resultslist&sort=plf-f&src=s&sid=d29218f01edc11e7bf35362dd2f7c5e9&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Best+proximity+point+in+F-metric+spaces+with+applications%22%29&sl=78&sessionSearchId=d29218f01edc11e7bf35362dd2f7c5e9&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000969675100001}{\mbox{[Web of Science]}} $
• [9] M. Zhou, N. Saleem, B. Ali, M.M. Misha and A.F.R. Lopez de Hierro, Common best proximity points and completeness of F-metric spaces, Mathematics, 11(2) (2023), 281. $ \href{https://doi.org/10.3390/math11020281}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85146778585&origin=resultslist&sort=plf-f&src=s&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Common+best+proximity+points+and+completeness+of+%22%29&sessionSearchId=502a560a04d6610739b2929b83131935&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000929408600001}{\mbox{[Web of Science]}} $
• [10] M. Alansari, S. Shagari and M.A. Azam, Fuzzy fixed point results in F-metric spaces with applications, J. Funct. Spaces, 2020 (2020), 5142815, 1-11. $ \href{https://doi.org/10.1155/2020/5142815}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85089150091&origin=resultslist&sort=plf-f&src=s&sid=d29218f01edc11e7bf35362dd2f7c5e9&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Fuzzy+fixed+point+results+in+F-metric+spaces+with+applications%22%29&sl=78&sessionSearchId=d29218f01edc11e7bf35362dd2f7c5e9&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000553451500001}{\mbox{[Web of Science]}} $
• [11] S.A. Mezel, J. Ahmad and G. Marino, Fixed point theorems for generalized (alpha-beta-psi)-contractions in F-metric spaces with applications, Mathematics, 8(4) (2020), 584, 1-14. $ \href{https://doi.org/10.3390/math8040584}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85084507317&origin=resultslist&sort=plf-f&src=s&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Contractions+in+F+-Metric+Spaces+with+Applications%22%29&sessionSearchId=502a560a04d6610739b2929b83131935&relpos=1}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000531824100124}{\mbox{[Web of Science]}} $
• [12] H. Faraji, N. Mirkov, Z.D. Mitrovic, R. Ramaswamy, O.A.A. Abdelnaby and S. Radenovic, Some new results for (a;b)-admissible mappings in F-metric spaces with applications to integral equations, Symmetry, 14(11) (2022), 2429, 1-13. $ \href{https://doi.org/10.3390/sym14112429}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85144719412&origin=resultslist&sort=plf-f&src=s&sid=d29218f01edc11e7bf35362dd2f7c5e9&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22admissible+mappings+in+F-metric+spaces+with+applications+to+integral+equations%22%29&sl=78&sessionSearchId=d29218f01edc11e7bf35362dd2f7c5e9&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000931804800001}{\mbox{[Web of Science]}} $
• [13] T. Kanwal, A. Hussain, H. Baghani and M. De la Sen, New fixed point theorems in orthogonal F-metric spaces with application to fractional differential equation, Symmetry, 12 (2020), 832, 1-15. $ \href{https://doi.org/10.3390/sym12050832}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85099926957&origin=resultslist&sort=plf-f&src=s&sid=d29218f01edc11e7bf35362dd2f7c5e9&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22New+fixed+point+theorems+in+orthogonal+F-metric+spaces+with+application+to+fractional+differential+equation%22%29&sl=78&sessionSearchId=d29218f01edc11e7bf35362dd2f7c5e9&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000540226400150}{\mbox{[Web of Science]}} $
• [14] B. Samet, C. Vetro and P. Vetro, Fixed point theorems for $\alpha-\psi$ contractive type mappings, Nonlinear Anal., 75(4) (2012), 2154–2165. $\href{https://doi.org/10.1016/j.na.2011.10.014}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-84655168090&origin=resultslist&sort=plf-f&src=s&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Fixed+point+theorems+for+%24%5Calpha-%5Cpsi%24+contractive+type+mappings%22%29&sessionSearchId=502a560a04d6610739b2929b83131935&relpos=9}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000298368600041}{\mbox{[Web of Science]}} $
• [15] R.P. Agarwal and D. O’Regan, Fixed point theory for admissible type maps with applications, Fixed Point Theory Appl., 2009 (2009), 439176, 1-22. $ \href{https://doi.org/10.1155/2009/439176}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-84872129002&origin=resultslist&sort=plf-f&src=s&sid=d29218f01edc11e7bf35362dd2f7c5e9&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Fixed+point+theory+for+admissible+type+maps+with+applications%22%29&sl=78&sessionSearchId=d29218f01edc11e7bf35362dd2f7c5e9&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000270535500001}{\mbox{[Web of Science]}} $
• [16] S. Chandok, Some fixed point theorems for alpha-beta- admissible Geraghty type contractive mappings and related results, Math. Sci., 9(3) (2015), 127-135. $ \href{https://doi.org/10.1007/s40096-015-0159-4}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-84990053088&origin=resultslist&sort=plf-f&src=s&sid=d29218f01edc11e7bf35362dd2f7c5e9&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Some+fixed+point+theorems+for+alpha-beta-+admissible+Geraghty+type+contractive+mappings+and+related+results%22%29&sl=78&sessionSearchId=d29218f01edc11e7bf35362dd2f7c5e9&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000367296300002}{\mbox{[Web of Science]}} $
• [17] R. Gubran, W.M. Alfaqih and M. Imdad, Common fixed point results for $\alpha$ admissible mappings via simulation function, J. Anal., 25(2) (2017), 281-290. $\href{http://dx.doi.org/10.1007/s41478-017-0056-3}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85087824108&origin=resultslist&sort=plf-f&src=s&sid=d29218f01edc11e7bf35362dd2f7c5e9&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Common+fixed+point+results+for+%24%5Calpha%24+admissible+mappings+via+simulation+function%22%29&sl=78&sessionSearchId=d29218f01edc11e7bf35362dd2f7c5e9&relpos=0}{\mbox{[Scopus]}} $
• [18] M. Öztürk and A. Büyükkaya, On some fixed point theorems for $\mathcal{G} (\Sigma, \vartheta, \Xi )$-contractions in modular b-metric spaces, Fundam. J.Math. Appl., 5(4) (2022), 210-227. $ \href{https://doi.org/10.33401/fujma.1107963}{\mbox{[CrossRef]}} $
• [19] V. Pazhani and M. Jeyaraman, Fixed point theorems in G-fuzzy convex metric spaces, Fundam. J. Math. Appl., 5(3) (2022), 145-151. $ \href{https://doi.org/10.33401/fujma.1034862}{\mbox{[CrossRef]}} $
• [20] V. Özturk and D. Türkoğlu, Fixed points for generalized a-y contractions in b-metric spaces, J. Nonlinear Convex Anal., 16(10) (2015), 2059-2066. $ \href{http://www.yokohamapublishers.jp/online-p/JNCA/vol16/jncav16n10p2059.pdf}{\mbox{[Web]}} $
• [21] A. Şahin, E. Özturk and G. Aggarwal, Some fixed-point results for the KF-iteration process in hyperbolic metric spaces, Symmetry, 15(7) (2023), 1360. $ \href{https://doi.org/10.3390/sym15071360}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85166333137&origin=resultslist&sort=plf-f&src=s&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22Some+fixed-point+results+for+the+KF-iteration+process+in+hyperbolic+metric+spaces%22%29&sessionSearchId=502a560a04d6610739b2929b83131935&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:001039707400001}{\mbox{[Web of Science]}} $
• [22] T. Tiwari and S. Thakur, Common fixed point theorem for pair of quasi triangular a-orbital admissible mappings in complete metric space with application, Malaya J. Mat., 11(02) (2023), 167-180. $ \href{https://doi.org/10.26637/mjm1102/006}{\mbox{[CrossRef]}}$
• [23] A. Asif, M. Nazam, M. Arshad and S.O.Kim, F-Metric, F-contraction and common fixed point theorems with applications, Mathematics, 7(7) (2019), 586, 1-13. $ \href{https://doi.org/10.3390/math7070586}{\mbox{[CrossRef]}} \href{https://www.scopus.com/record/display.uri?eid=2-s2.0-85068882890&origin=resultslist&sort=plf-f&src=s&sid=d29218f01edc11e7bf35362dd2f7c5e9&sot=b&sdt=b&s=TITLE-ABS-KEY%28%22contraction+and+common+fixed+point+theorems+with+applications%22%29&sl=78&sessionSearchId=d29218f01edc11e7bf35362dd2f7c5e9&relpos=0}{\mbox{[Scopus]}} \href{https://www.webofscience.com/wos/woscc/full-record/WOS:000478765700025}{\mbox{[Web of Science]}} $