Nonlinear Contraction Mappings in b-metric Space and Related Fixed Point Results with Application
Muhammed Raji
1
(Department of Mathematics, Federal University Lokoja, Lokoja, Nigeria)
Arvind Kumar Rajpoot
2
(Department of Mathematics Aligarh Muslim University Aligarh 202002, India)
Laxmi Rathour
3
(Department of Mathematics,Indira Gandhi National Tribal University, Lalpur, Amarkantak, Anuppur, Madhya Pradesh 484 887, India)
Lakshmi Narayan Mishra
4
(Department of Mathematics School of Advanced Sciences, Vellore Institute of Technology, Vellore 632 014 Tamil Nadu, India)
Vishnu Narayan Mishra
5
(Department of Mathematics,Indira Gandhi National Tribal University,Lalpur, Amarkantak, Anuppur, Madhya Pradesh 484 887, India)
کلید واژه: Fixed point, coincidence point, Eldeisten-Suzuki-type contraction, b-metric space,
چکیده مقاله :
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.
چکیده انگلیسی :
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 operations 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] Boriceanu M. Strict fixed point theorems for multivalued operators in b-metric Spaces. International Journal of Modern Mathematical Sciences. 2009; 4(3): 285-301.
[3] 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
[4] Czerwik S. Contraction mappings in b-metric spaces. Acta mathematica et informatica universitatis ostraviensis. 1993; 1(1): 5-11.
[5] Czerwik S. Nonlinear set-valued contraction mappings in b-metric spaces. Atti Sem. Mat. Univ. Modena. 1998; 46: 263-276.
[6] 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
[7] 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
[8] 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
[9] 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
[10] Kannan R. Some results on fixed points. Bull Calcutta Math Soc. 1968; 60: 71-76. DOI: https://doi.org/10.2307/2316437
[11] 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
[12] Nieto JJ, Pouso RL, Rodrguez-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
[13] Nieto JJ, Rodrguez-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
[14] Nieto JJ, Rodrguez-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
[15] Paesano D, Vetro P. Suzukis 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
[16] 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
[17] 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
[18] 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
[19] 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
[20] 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
[21] 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
[22] 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
[23] Rus I A, Petrusel A, Petrusel G. Fixed Point Theory. Cluj-Napoca: Cluj University Press; 2(2), 2008.
[24] 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
[25] 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
[26] 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
