Volume 5, Issue 9 (September 2018), Pages: 1-5
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Original Research Paper
Title: Fixed point results for two pairs of non-self hybrid mappings in metric spaces of hyperbolic type
Author(s): Kanayo Stella Eke *, Hudson Akewe
Affiliation(s):
Department of Mathematics, Covenant University, Canaanland, KM 10 Idiroko Road, P. M. B. 1023, Ota, Ogun State, Nigeria
https://doi.org/10.21833/ijaas.2018.09.001
Full Text - PDF XML
Abstract:
This research paper proves some interesting results on common fixed point for two pairs of non-self hybrid (single valued and multivalued) contractive mappings in metric spaces of hyperbolic type. The results are established without employing the weakly commutativity and continuity assumptions. We adopted an existing method of proof to obtain our results. The results generalize and improve some results proved in related works in literature. An example is given to validate our claim.
© 2018 The Authors. Published by IASE.
This is an open access article under the CC BY-NC-ND license (http://creativecommons.org/licenses/by-nc-nd/4.0/).
Keywords: Metric space of hyperbolic type, Non-self mappings, Hybrid mappings, Common fixed points
Article History: Received 9 January 2018, Received in revised form 18 May 2018, Accepted 20 June 2018
Digital Object Identifier:
https://doi.org/10.21833/ijaas.2018.09.001
Citation:
Eke KS and Akewe H (2018). Fixed point results for two pairs of non-self hybrid mappings in metric spaces of hyperbolic type. International Journal of Advanced and Applied Sciences, 5(9): 1-5
Permanent Link:
http://www.science-gate.com/IJAAS/2018/V5I9/Eke.html
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References (17)
- Ahmed A and Imdad M (1998). Some common fixed point theorems for mappings and multi-valued mappings. Journal of Mathematical Analysis and Applications, 218(2): 546-560. https://doi.org/10.1006/jmaa.1997.5738 [Google Scholar]
- Ahmed A and Khan AR (1997). Some common fixed point theorems for non-self hybrid contractions. Journal of Mathematical Analysis and Applications, 213(1): 275-286. https://doi.org/10.1006/jmaa.1997.5537 [Google Scholar]
- Assad N and Kirk W (1972). Fixed point theorems for set-valued mappings of contractive type. Pacific Journal of Mathematics, 43(3): 553-562. https://doi.org/10.2140/pjm.1972.43.553 [Google Scholar]
- Banach S (1922). Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales. Fundamenta Mathematicae Peer-Reviewed Journal, 3(1): 133-181. https://doi.org/10.4064/fm-3-1-133-181 [Google Scholar]
- Bishop SA, Ayoola EO, and Oghonyon GJ (2017). Existence of mild solution of impulsive quantum stochastic differential equation with nonlocal conditions. Analysis and Mathematical Physics, 7(3): 255-265. https://doi.org/10.1007/s13324-016-0140-x [Google Scholar]
- Ciric L and Cakić N (2009). On common fixed point theorems for non-self hybrid mappings in convex metric spaces. Applied Mathematics and Computation, 208(1): 90-97. https://doi.org/10.1016/j.amc.2008.11.012 [Google Scholar]
- Ciric LB, Ume JS, and Nikolić NT (2007). On two pairs of non-self hybrid mappings. Journal of the Australian Mathematical Society, 83(1): 17-30. https://doi.org/10.1017/S1446788700036363 [Google Scholar]
- Eke K (2016). Common fixed point theorems for weakly compatible non-self mappings in metric spaces of hyperbolic type. Global Journal of Mathematical Analysis, 4(1): 2-5. https://doi.org/10.14419/gjma.v4i1.5733 [Google Scholar]
- Eke KS, Davvaz B, and Oghonyon JG (2018). Common fixed point theorem for nonself mappings of nonlinear contractive maps in convex metric spaces. Journal of Mathematics and Computer Sciences, 18: 184-191. https://doi.org/10.22436/jmcs.018.02.06 [Google Scholar]
- Frechet MM (1906). Sur quelques points du calcul fonctionnel. Rendiconti del Circolo Matematico di Palermo (1884-1940), 22(1): 1-72. [Google Scholar]
- Huang X, Luo J, Zhu C, and Wen X (2014). Common fixed point theorem for two pairs of non-self-mappings satisfying generalized Ćirić type contraction condition in cone metric spaces. Fixed Point Theory and Applications, 2014(1): 157-176. https://doi.org/10.1186/1687-1812-2014-157 [Google Scholar]
- Itoh S (1977). Multivalued generalized contractions and fixed point theorems. Commentationes Mathematicae Universitatis Carolinae, 18(2): 247-258. [Google Scholar]
- Kirk WA (1982). Krasnoselskii's iteration process in hyperbolic space. Numerical Functional Analysis and Optimization, 4(4): 371-381. https://doi.org/10.1080/01630568208816123 [Google Scholar]
- Nadler S (1969). Multi-valued contraction mappings. Pacific Journal of Mathematics, 30(2): 475-488. https://doi.org/10.2140/pjm.1969.30.475 [Google Scholar]
- Okeke GA and Abbas M (2015). Convergence and almost sure T-stability for a random iterative sequence generated by a generalized random operator. Journal of Inequalities and Applications, 2015(1): 146-157. https://doi.org/10.1186/s13660-015-0666-8 [Google Scholar]
- Okeke GA and Kim JK (2015). Convergence and summable almost T-stability of the random Picard-Mann hybrid iterative process. Journal of Inequalities and Applications, 2015(1): 290-304. https://doi.org/10.1186/s13660-015-0815-0 [Google Scholar]
- Takahashi W (1970). A convexity in metric space and nonexpansive mappings, I. In the Kodai Mathematical Seminar Reports, Department of Mathematics, Tokyo Institute of Technology, Tokyo, Japan, 22(2): 142-149. [Google Scholar]
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