Fixed Point Theorems in Uniform Space and Its Applications
DOI:
https://doi.org/10.32628/IJSRST25125102Keywords:
Common fixed point, Hausdorff Uniform spaces, E & A-Distance, weakly compatible maps, admissible mappings, simulation functionsAbstract
In this study, we use the notation of E-distance in uniform space to prove certain popular fixed-point theorems for pairs of weakly and semi-compatible mappings. For a pair of self-mappings in Hausdorff uniform spaces, we prove various stability results for a few common fixed points. Our findings enhance and generalize some of the established stability findings in the literature. Classification of Mathematics Subjects: 47H10, 49H10, 54H25.
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B.K. Sharma, D.R. Sahu and, Y. J. Cho, Semi compatibility and fixed points, Math. Japon, 42(1995), no.1, 91-98.
B.K. Rhoades and G. Jujck, Fixed points for set valued functions without continuity, Indian J. Pure Appl. Math. 29(1998), no. 3, 227-238.
D. Moutawakil and M. Aamri, Weak compatibility and common fixed-point theorems for A-contractive and E- Expansive maps in uniform spaces, Serdica Math. J. 31(2005), 75-86.
Khojasteh, F., Shukla, S. & Radenovic, S. A new approach to the study of fixed-point theory for simulation functions. Filomat. 29(6), 1189–1194 (2015). DOI: https://doi.org/10.2298/FIL1506189K
Aydi, H. & Felhi, A. Fixed points in modular spaces via α-admissible mappings and simulation functions. Journal of Nonlinear Science and Applications 9, 3686–3701 (2016). DOI: https://doi.org/10.22436/jnsa.009.06.20
Karapinar, E. Fixed points result via simulation functions. Filomat. 30(8), 2343–2350 (2016). DOI: https://doi.org/10.2298/FIL1608343K
Rodrigues-Montes, J. & Charris, J. A. Fixed points for W-contractive or W-expansive maps in uniform spaces: toward a unified approach. Southwest journal of Pure and Applied Mathematics 1, 93– 101 (2001).
Umudu, J. C., Olaleru, J. O. & Mogbademu, A. A. Best proximity points result for Geraghty p- proximal cyclic quasi-contraction in uniform spaces. Divulgaciones Matematicas 21(1-2), 21– 31 (2020). DOI: https://doi.org/10.1186/s13663-020-00683-z
Samet, B., Vetro, C. & Vetro, P. Fixed point theorems for α-ψ-contractive mappings. Nonlinear Analysis 75, 2154–2165 (2012). DOI: https://doi.org/10.1016/j.na.2011.10.014
Bourbaki, N. Topologie Generale, Chapitre 1: Structures Topologies, Chapitre 2: Structures Uniformes. Quatrieme Edition. Actualites Scientifique set Industrielles, Hermann, Paris, France.1142, (1965)
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