Nonlinear Contraction Mappings in b-metric Space and Related Fixed Point Results with Application
الموضوعات : Transactions on Fuzzy Sets and Systems
Muhammed Raji
1
,
Arvind Kumar Rajpoot
2
,
Laxmi Rathour
3
,
Lakshmi Narayan Mishra
4
,
Vishnu Narayan Mishra
5
1 - Department of Mathematics, Confluence University of Science and Technology, Osara, Kogi State, Nigeria.
2 - Department of Mathematics, Aligarh Muslim University, Aligarh 202002, India.
3 - Department of Mathematics, National Institute of Technology, Chaltlang, Aizawl 796 012, Mizoram, India.
4 - Department of Mathematics, School of Advanced Sciences, Vellore Institute of Technology, Vellore 632 014, Tamil Nadu, India.
5 - Department of Mathematics, Indira Gandhi National Tribal University, Lalpur, Amarkantak, Anuppur, Madhya Pradesh 484 887, India.
الکلمات المفتاحية: Fixed point, Coincidence point, Eldeisten-Suzuki-type contraction, b-metric space,
ملخص المقالة :
The paper aims to introduce some fixed point results in the setting of sequential compact b-metric spaces to prove Eldeisten-Suzuki-type contraction for self-mappings. These contributions extend the existing literature on fixed point for ordered metric spaces and fixed point theory. Through illustrative examples, we showcase the practical applicability of our proposed notions and results, demonstrating their effectiveness in real-world scenarios.
[1] Banach S. Sur les op´erations dans les ensembles abstraits et leur application aux equations itegrales. Fundamenta mathematicae. 1922; 3(1): 133-181. DOI: https://doi.org/10.4064/fm-3-1-133-181
[2] Ran ACM, Reurings MCB. A fixed point theorem in partially ordered sets and some applications to matrix equations. proceedings of the American Mathematical Society. 2004; 132(5): 1435-1443. https://www.ams.org/journals/proc/2004-132-05/S0002-9939-03-07220-4/S0002-9939-03-07220-4.pdf
[3] Nieto JJ, Rodrıguez-Lopez R. Existence and uniqueness of fixed point in partially ordered sets and applications to ordinary differential equations. Acta Mathematica Sinica, English Series. 2007; 23(12): 2205-2212. DOI: https://doi.org/10.1007/s10114-005-0769-0
[4] Rus I A, Petru¸sel A, Petru¸sel G. Fixed Point Theory. Cluj-Napoca: Cluj University Press; 2(2), 2008.
[5] Raji M, Ibrahim MA. Fixed point theorems for fuzzy contractions mappings in a dislocated bmetric spaces with applications. Annals of Mathematics and Computer Science. 2024; 21: 1-13. DOI: https://doi.org/10.56947/amcs.v21.233
[6] Shah MH, Hussain N. Nonlinear contractions in partially ordered quasi b-metric spaces. Communications of the Korean Mathematical Society. 2012; 27(1): 117-128. DOI: http://dx.doi.org/10.4134/CKMS.2012.27.1.117
[7] Kannan R. Some results on fixed points. Bull Calcutta Math Soc. 1968; 60: 71-76. DOI: https://doi.org/10.2307/2316437
[8] Raji M, Ibrahim MA, Rauf K, Kehinde R. Common fixed point results for fuzzy Fcontractive mappings in a dislocated metric spaces with application. Qeios. 2024; 7; 1-21. DOI: https://doi.org/10.32388/SV98CN
[9] Dewangan K, Rathour L, Mishra VN, Raiz M. On multi-valued nonexpansive mappings in UCBS, Journal of Computational Analysis and Applications. 2024; 33(1): 396-406. https://eudoxuspress.com/index.php/pub/article/view/31
[10] Mishra LN, Raiz M, Rathour L, Mishra VN. Tauberian Theorems for Weighted Means of Double Sequences in Intuitionistic Fuzzy Normed Spaces. Yugoslav Journal of Operations Research. 2022; 377-388. DOI: https://doi.org/10.2298/YJOR210915005M
[11] Czerwik S. Contraction mappings in b-metric spaces. Acta mathematica et informatica universitatis ostraviensis. 1993; 1(1): 5-11.
[12] Boriceanu M. Strict fixed point theorems for multivalued operators in b-metric Spaces. International Journal of Modern Mathematical Sciences. 2009; 4(3): 285-301.
[13] Hussain N, Doric D, Kadelburg Z, Radenovic S. Suzuki-type fixed point results in metric type spaces. Fixed point theory and applications. 2012; 2012: 1-12. DOI: https://doi.org/10.1186/1687-1812-2012-126
[14] Edelstein M. On fixed and periodic points under contractive mappings. Journal of the London Mathematical Society. 1962; 1(1): 74-79. DOI: https://doi.org/10.1112/jlms/s1-37.1.74
[15] Suzuki T. A new type of fixed point theorem in metric spaces. Nonlinear Analysis: Theory, Methods & Applications. 2009; 71(11): 5313-5317. DOI: https://doi.org/10.1016/j.na.2009.04.017
[16] Doric D, Kadelburg Z, Radenovic S. Edelstein-Suzuki-type fixed point results in metric and abstract metric spaces.Nonlinear Analysis: Theory, Methods & Applications. 2012; 75(4): 1927-1932. DOI: https://doi.org/10.1016/j.na.2011.09.046
[17] Paesano D, Vetro P. Suzuki’s type characterizations of completeness for partial metric spaces and fixed points for partially ordered metric spaces. Topology and its Applications. 2012; 159(3): 911-920. DOI:
https://doi.org/10.1016/j.topol.2011.12.008
[18] Salimi P, Karapinar E. Suzuki-Edelstein type contractions via auxiliary functions. Mathematical Problems in Engineering. 2013; 2013(1): 648528. DOI: https://doi.org/10.1155/2013/648528
[19] Radenovic S, Salimi P, Vetro C, Dosenovic T. Edelstein-Suzuki-type results for self-mappings in various abstract spaces with application to functional equations. Acta Mathematica Scientia. 36(1): 94-110. DOI:
https://doi.org/10.1016/S0252-9602(15)30081-3
[20] Cosentino M, Salimi P, Vetro P. Fixed point results on metric-type spaces. Acta Mathematica Scientia. 2014; 34(4):1237-1253. DOI: https://doi.org/10.1016/S0252-9602(14)60082-5
[21] Czerwik S. Nonlinear set-valued contraction mappings in b-metric spaces. Atti Sem. Mat. Univ. Modena. 1998; 46: 263-276.
[22] Nieto JJ, Rodrıguez-Lopez R. Contractive mapping theorems in partially ordered sets and applications to ordinary differential equations. Order. 2005; 22: 223-239. DOI: https://doi.org/10.1007/s11083-005- 9018-5
[23] Raji M, Rathour L, Mishra LN, Mishra VN. Generalized twisted (α, β)-ψ contractive type mappings and related fixed point results with applications. Int. J. Adv. Sci. Eng. 2024; 10(4): 3639-3654. DOI:
https://doi.org/10.29294/IJASE.10.4.2024.3639-3654
[24] Raji M. Generalized α-ψ contractive type mappings and related coincidence fixed point theorems with applications.The Journal of Analysis. 2023; 31(2): 1241-1256. DOI: https://doi.org/10.1007/s41478-022- 00498-8
[25] Raji M, Ibrahim MA. Fixed point theorems for modified F-weak contractions via α- admissible mapping with application to periodic points. Annals of Mathematics and Computer Science. 2024; 20: 82-97. DOI:
https://doi.org/10.56947/amcs.v20.232
[26] Nieto JJ, Pouso RL, Rodrıguez-Lopez R. Fixed point theorems in ordered abstract spaces. Proceedings of the American Mathematical Society. 2007; 135(8): 2505-2517. DOI: https://doi.org/10.1090/S0002- 9939-07-08729-1
