호남수학학술지 (Honam Mathematical Journal)

  • 제40권4호
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  • Pages.719-732
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  • 2018
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  • 1225-293X(pISSN)
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  • 2288-6176(eISSN)
호남수학회 (The Honam Mathematical Society)
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HYBRID FIXED POINT RESULTS VIA E.A AND TANGENTIAL PROPERTIES IN METRIC SPACES

  • 투고 : 2018.05.08
  • 심사 : 2018.09.06
  • 발행 : 2018.12.25
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초록

In this manuscript, hybrid fixed point results for four maps using (E.A) and tangential properties in the setting of metric space are studied. Application to system of functional equations is also studied.

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참고문헌

  1. M. Abbas and B.E. Rhoades, Common fixed point theorems for hybrid pairs of occasionally weakly compatible mappings satisfying generalized contractive condition of integral type. Fixed Point Theory Appl. 2007, Art. ID 54101, 9 pp.
  2. A. Latif, N. Hussain and J. Ahmad, Coincidence points for hybrid contractions in cone metric spaces. J. Nonlinear Convex Anal. 17 (2016), no. 5, 899-906.
  3. M.A. Al-Thagafi and N. Shahzad, Generalized I -nonexpansive selfmaps and invariant approximations. Acta Math. Sin. (Engl. Ser.) 24 (2008), no. 5, 867-876. https://doi.org/10.1007/s10114-007-5598-x
  4. M. Aamri and D. El Moutawakil, Some new common fixed point theorems under strict contractive conditions. J. Math. Anal. Appl. 270 (2002), no. 1, 181-188. https://doi.org/10.1016/S0022-247X(02)00059-8
  5. Z. Mustafa, H. Aydi and E. Karap?nar, On common fixed points in G -metric spaces using (E:A) property. Comput. Math. Appl. 64 (2012), no. 6, 1944-1956. https://doi.org/10.1016/j.camwa.2012.03.051
  6. G. V. R. Babu and G.N. Alemayehu, Common fixed point theorems for occasionally weakly compatible maps satisfying property (E:A) using an inequality involving quadratic terms. Appl. Math. Lett. 24 (2011), no. 6, 975-981. https://doi.org/10.1016/j.aml.2011.01.008
  7. A. Branciari, A fixed point theorem for mappings satisfying a general contractive condition of integral type. Int. J. Math. Math. Sci. 29 (2002), no. 9, 531-536. https://doi.org/10.1155/S0161171202007524
  8. S. Chauhan, M. Imdad, E. Karapinar and B. Fisher, An integral type fixed point theorem for multi-valued mappings employing strongly tangential property. J. Egyptian Math. Soc. 22 (2014), no. 2, 258-264. https://doi.org/10.1016/j.joems.2013.08.002
  9. S. Itoh and W. Takahashi, Single-valued mappings, multivalued mappings and fixed-point theorems. J. Math. Anal. Appl. 59 (1977), no. 3, 514-521. https://doi.org/10.1016/0022-247X(77)90078-6
  10. G. Jungck, Common fixed points for noncontinuous nonself maps on nonmetric spaces. Far East J. Math. Sci. 4 (1996), no. 2, 199-215.
  11. G. Jungck and B.E. Rhoades, Fixed points for set valued functions without continuity. Indian J. Pure Appl. Math. 29 (1998), no. 3, 227-238.
  12. G. Jungck, Compatible mappings and common fixed points. Internat. J. Math. Math. Sci. 9 (1986), no. 4, 771-779. https://doi.org/10.1155/S0161171286000935
  13. T. Kamran, Coincidence and fixed points for hybrid strict contractions. J. Math. Anal. Appl. 299 (2004), no. 1, 235-241. https://doi.org/10.1016/j.jmaa.2004.06.047
  14. T. Kamran and N. Cakic, Hybrid tangential property and coincidence point theorems. Fixed Point Theory 9 (2008), no. 2, 487-496.
  15. H. Kaneko and S. Sessa, Fixed point theorems for compatible multi-valued and single-valued mappings. Internat. J. Math. Math. Sci. 12 (1989), no. 2, 257-262. https://doi.org/10.1155/S0161171289000293
  16. M. S. Khan, M. Swaleh and S. Sessa, Fixed point theorems by altering distances between the points. Bull. Austral. Math. Soc. 30 (1984), no. 1, 1-9. https://doi.org/10.1017/S0004972700001659
  17. Z. Liu, X. Li, S.M. Kang and S.Y. Cho, Fixed point theorems for mappings satisfying contractive conditions of integral type and applications. Fixed Point Theory Appl. 2011, 2011:64, 18 pp. https://doi.org/10.1186/1687-1812-2011-18
  18. Z. Liu, B. Xu and S. M. Kang, Two fixed point Theorems of mappings satisfying contractive inequalities of integral type. Int. J. Pure. Appl. Math. 90, 2014 85-100, 90pp.
  19. Z. Liu and S.M. Kang, Existence and uniqueness of solutions for two classes of functional equations arising in dynamic programming. Acta Math. Appl. Sin. Engl. Ser. 23 (2007), no. 2, 195-208. https://doi.org/10.1007/s10255-007-0363-6
  20. Y. Liu, J. Wu and Z. Li, Zhixiang, Common fixed points of single-valued and multivalued maps. Int. J. Math. Math. Sci. 2005, no. 19, 3045-3055.
  21. Jr. S. B., Multi-valued contraction mappings. Pacific J. Math. 30 1969 475-488. https://doi.org/10.2140/pjm.1969.30.475
  22. V. Parvaneh, H. Hosseinzadeh, N. Hussain and L. Ciric, PPF dependent fixed point results for hybrid rational and Suzuki-Edelstein type contractions in Banach spaces. Filomat 30 (2016), no. 5, 1339-1351. https://doi.org/10.2298/FIL1605339P
  23. R. P. Pant, Common fixed points of noncommuting mappings. J. Math. Anal. Appl. 188 (1994), no. 2, 436-440. https://doi.org/10.1006/jmaa.1994.1437
  24. R. P. Pant, Common fixed points of Lipschitz type mapping pairs. J. Math. Anal. Appl. 240 (1999), no. 1, 280-283. https://doi.org/10.1006/jmaa.1999.6559
  25. K. P. R. Sastry and I. S. R. Krishna Murthy, Common fixed points of two partially commuting tangential selfmaps on a metric space. J. Math. Anal. Appl. 250 (2000), no. 2, 731-734. https://doi.org/10.1006/jmaa.2000.7082
  26. W. Sintunavarat and P. Kumam, Coincidence and common fixed points for hybrid strict contractions without the weakly commuting condition. Appl. Math. Lett. 22 (2009), no. 12, 1877-1881. https://doi.org/10.1016/j.aml.2009.07.015
  27. W. Sintunavarat and P. Kumam, Gregus-type common fixed point theorems for tangential multivalued mappings of integral type in metric spaces. Int. J. Math. Math. Sci. 2011, Art. ID 923458, 12 pp.
  28. S. L. Singh and S.N. Mishra, SCoincidences and fixed points of nonself hybrid contractions. J. Math. Anal. Appl. 256 (2001), no. 2, 486-497. https://doi.org/10.1006/jmaa.2000.7301
  29. S. Sessa, SOn a weak commutativity condition of mappings in fixed point considerations. Publ. Inst. Math. (Beograd) (N.S.) 32(46) (1982), 149-153.
  30. M. Samreen, T. Kamran, and E. Karapinar, Fixed point theorems for hybrid mapping. The Scientific World Journal. (2015), Article ID 938165, 7pp.