Coupled Fixed Point Problem in Abstract Convex Spaces
DOI:
https://doi.org/10.26713/jims.v12i4.1498Keywords:
Abstract convex space, KKM theorem, Partial KKM space, Coupled fixed point problemAbstract
We establish some existence results for a generalized coupled coincidence point problem (for short, (GCCP)) in abstract convex spaces. The solvability of the GCCP is presented by using our KKM theory. Also, we derive the results on coupled coincidence points and coupled fixed points, which were studied by Lakshmikantham and Ciric, Amini-Harandi, and Mitrovic.
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N. Altwaijry, S. Ounaies and S. Chebbi, Generalized convexity and applications to fixed points and equilibria, Journal of Fixed Point Theory and Applications 20 (2018), Article number 31, DOI: 10.1007/s11784-018-0517-6.
A. Amini-Harandi, Best and coupled best approximations theorems in abstract convex spaces, Nonlinear Analysis: Theory, Methods & Applications 74 (2011), 922 – 926, DOI: 10.1016/j.na.2010.09.045.
H. Ben-El-Mechaiekh, S. Chebbi, M. Florenzano and J. V. Llinares, A fixed point theorem without convexity, Working Paper 97-22 Economics Series (11 April 1997), Departamento de Economia Universidad Carlos ill de Madrid CaIle Madrid, 126 28903 Getafe (Spain), URL: https://e-archivo.uc3m.es/bitstream/handle/10016/6022/we972211.PDF?sequence=1&isAllowed=y.
T. G. Bhaskar and V. Lakshmikantham, Fixed point theorems in partially ordered metric spaces and applications, Nonlinear Analysis: Theory, Methods & Applications 65 (2006), 1379 – 1393, DOI: 10.1016/j.na.2005.10.017.
D. Guo and V. Lakshmikantham, Coupled fixed points of nonlinear operators with applications, Nonlinear Analysis: Theory, Methods & Applications 11(5) (1987), 623 – 632, DOI: 10.1016/0362-546X(87)90077-0.
C. D. Horvath, A note on metric spaces with continuous midpoints, Annals of the Academy of Romanian Scientists, Series on Mathematics and its Applications 1(2) (2009), 252 – 288, URL: http://www.aos.ro/wp-content/anale/MVol1Nr2Art.5.pdf.
E. Karapinar, S. I. Moustafa, A. Shehata and R. P. Agarwal, Fractional hybrid differential equations and coupled fixed-point results for ®-admissible F(íƒ1,íƒ2)-contractions in M-metric spaces, Discrete Dynamics in Nature and Society 2020 (2020), Article ID 7126045, 13 pages, DOI: 10.1155/2020/7126045.
W. Kulpa and A. Szymanski, A note on n-continuous L¤-operators, Topology Proceedings 37 (2011), 403–407, URL: http://topology.auburn.edu/tp/reprints/v37/tp37023.pdf.
V. Lakshmikantham and L. C´ iric´, Coupled fixed point theorems for nonlinear contractions in partially ordered metric spaces, Nonlinear Analysis: Theory, Methods & Applications 70 (2009), 4341 – 4349, DOI: 10.1016/j.na.2008.09.020.
Z. D. Mitrovi´c, A coupled best approximations theorem in normed spaces, Nonlinear Analysis: Theory, Methods & Applications 72 (2010), 4049 – 4052, DOI: 10.1016/j.na.2010.01.035.
Z. D. Mitrovi´c, On a coupled fixed point problem in topological vector spaces, Mathematical and Computer Modelling 57 (2013), 2388 – 2392, DOI: 10.1016/j.mcm.2011.12.040.
C. P. Niculescu and L. Roven¸ta, Fan's inequality in geodesic spaces, Applied Mathematics Letters 22 (2009), 1529 – 1533, DOI: 10.1016/j.aml.2009.03.020.
K. Nikodem, K-convex and K-concave Set-valued Functions, Politechnika, Lodzka (1989).
S. Park, General KKM theorems for abstract convex spaces, Journal of Informatics & Mathematical Sciences 1(1) (2009), 1 – 13, DOI: 10.26713/jims.v1i1.3.
S. Park, The KKM principle in abstract convex spaces: equivalent formulations and applications, Nonlinear Analysis: Theory, Methods & Applications 73 (2010), 1028 – 1042, DOI: 10.1016/j.na.2010.04.029.
S. Park, Various examples of the KKM spaces, Journal of Nonlinear and Convex Analysis 21(1) (2020), 1 – 19, URL: https://www.researchgate.net/publication/338254859_VARIOUS_EXAMPLES_OF_THE_KKM_SPACES, (presented at IWNAO2018).
S. Park, From Hadamard manifolds to Horvath spaces, Journal of National Academy of Sciences, Republic of Korea, National Science Series 58(1) (2019), 1 – 24, URL: https://www.researchgate.net/profile/Sehie_Park/publication/331859591_From_Hadamard_Manifolds_to_Horvath_Spaces_JNAS-ROK_2019/links/5d23ff6e92851cf440728143/From-Hadamard-Manifolds-to-Horvath-Spaces-JNAS-ROK-2019.pdf.
S. Park, Riemannian manifolds are KKM spaces, Advances in the Theory of Nonlinear Analysis and its Application 3(2) (2019), 64 – 73, DOI: 10.31197/atnaa.513857.
S. Park, B-spaces are KKM spaces, Journal of Nonlinear and Convex Analysis 20(4) (2019), 739 – 746, URL: https://www.researchgate.net/profile/Sehie_Park/publication/335690725_B-SPACES_ARE_KKM_SPACES/links/5d7c394d4585155f1e4c1b6f/B-SPACES-ARE-KKM-SPACES.pdf.
S. Park, Extending the realm of Horvath spaces, Journal of Nonlinear and Convex Analysis 20(8) (2019), 1609 – 1621, URL: https://www.researchgate.net/profile/Sehie_Park/publication/336738968_EXTENDING_THE_REALM_OF_HORVATH_SPACES/links/5dcdec2192851c382f3dfece/EXTENDING-THE-REALM-OF-HORVATH-SPACES.pdf.
S. Park, On further examples of partial KKM spaces, Journal of Fixed Point Theory 2019 (2019), Article ID 10, 1 – 18, URL: http://jfpt.scik.org/issues/201910.pdf.
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