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ĆIRIĆ TYPE ALPHA-PSI F-CONTRACTION INVOLVING FIXED POINT ON A CLOSED BALL

  • Hussain, Aftab (Department of Mathematics, Khwaja Fareed University of Engineering & Information Technology)
  • 투고 : 2017.09.25
  • 심사 : 2019.01.03
  • 발행 : 2019.03.25

초록

The article is written with a view to introducing the new idea of an F-contraction on a closed ball and have new ${\acute{C}}iri{\acute{c}}$ type fixed point theorems in the framework of a complete metric space. That is why this outcome becomes useful for the contraction of the mapping on a closed ball instead of the whole space. At the same time, some comparative examples are constructed which establish the superiority of our results. It can be stated that the results that have come into being give proof of extension as well as substantial generalizations and improvements of several well known results in the existing comparable literature.

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참고문헌

  1. M. Abbas and T. Nazir, Common fixed point of a power graphic contraction pair in partial metric spaces endowed with a graph, Fixed Point Theory Appl. (2013), 2013:20. https://doi.org/10.1186/1687-1812-2013-20
  2. M. Abbas, B. Ali and S. Romaguera, Fixed and periodic points of generalized contractions in metric spaces, Fixed Point Theory Appl. (2013), 2013:243. https://doi.org/10.1186/1687-1812-2013-243
  3. T. Abdeljawad, Meir-Keeler ${\alpha}$-contractive fixed and common fixed point theorems, Fixed Point Theory Appl. (2013), doi:10.1186/1687-1812-2013-19.
  4. O. Acar and I. Altun, A fixed point theorem for multivalued mappings with ${\delta}$-Distance, Abstr. Appl. Anal., (2014), Article ID 497092, 5 pages.
  5. J. Ahmad, A. Al-Rawashdeh, A. Azam, Some new fixed point theorems for generalized F-contractions in complete metric spaces, Fixed Point Theory Appl. (2015), 2015:80. https://doi.org/10.1186/s13663-015-0333-2
  6. M. Arshad , Fahimuddin, A. Shoaib and A. Hussain, Fixed point results for ${\alpha}-{\psi}$-locally graphic contraction in dislocated qusai metric spaces, Math Sci., (2014), doi 10.1007/s40096-014-0132, 7 pages.
  7. M. Arshad , A. Shoaib, I. Beg, Fixed point of a pair of contractive dominated mappings on a closed ball in an ordered complete dislocated metric space, Fixed Point Theory Appl. (2013), 2013:115. https://doi.org/10.1186/1687-1812-2013-115
  8. M. Arshad, A. Shoaib, and P. Vetro, Common fixed points of a pair of Hardy Rogers type mappings on a closed ball in ordered dislocated metric spaces, Journal of Function Spaces, 2013 (2013), article ID 638181, 9 pages.
  9. M. Arshad, S. Khan and J Ahmad, Fixed point results for F-contractions involving some new rational expressions, JP Journal of Fixed Point Theory and Applications, 11(1) (2016), 79-97. https://doi.org/10.17654/FP011010079
  10. A. Azam, S. Hussain and M. Arshad, Common fixed points of Chatterjea type fuzzy mappings on closed balls, Neural Computing & Applications, (2012), 21 (Suppl 1):S313-S317. https://doi.org/10.1007/s00521-012-0907-4
  11. A. Azam, M. Waseem, M. Rashid, Fixed point theorems for fuzzy contractive mappings in quasi-pseudo-metric spaces, Fixed Point Theory Appl. (2013), 2013:27. https://doi.org/10.1186/1687-1812-2013-27
  12. S.Banach, Sur les operations dans les ensembles abstraits et leur application aux equations itegrales, Fund. Math., 3 (1922), 133-181. https://doi.org/10.4064/fm-3-1-133-181
  13. F. Bojor, Fixed point theorems for Reich type contraction on metric spaces with a graph, Nonlinear Anal., 75 (2012), 3895-3901. https://doi.org/10.1016/j.na.2012.02.009
  14. LB. Ciric, A generalization of Banach's contraction principle, Proc. Am. Math. Soc., 45 (1974), 267-273 https://doi.org/10.1090/S0002-9939-1974-0356011-2
  15. M. Cosentino, P. Vetro, Fixed point results for F-contractive mappings of Hardy-Rogers-Type, Filomat 28(4) (2014), 715-722. https://doi.org/10.2298/FIL1404715C
  16. M. Edelstein, On fixed and periodic points under contractive mappings, J. Lond. Math. Soc., 37 (1962), 74-79. https://doi.org/10.1112/jlms/s1-37.1.74
  17. B. Fisher, Set-valued mappings on metric spaces, Fundamenta Mathematicae, 112(2) (1981), 141-145. https://doi.org/10.4064/fm-112-2-141-145
  18. M. Geraghty, On contractive mappings, Proc. Amer. Math. Soc., 40 (1973), 604-608. https://doi.org/10.1090/S0002-9939-1973-0334176-5
  19. A. Hussain and M. Arshad, New type of multivalued F-Contraction involving fixed Point on Closed Ball, J. Math. Comp. Sci. 10 (2017), 246-254.
  20. A. Hussain, M. Arshad and Sami Ullah Khan,  $\tau$-Generalization of Fixed Point Results for F-Contractions, Bangmod Int. J. Math & Comp. Sci. 1(1) (2015), 136-146.
  21. N. Hussain , J. Ahmad and A. Azam , On Suzuki-Wardowski type fixed point theorems, The Journal of Nonlinear Sciences and Applications, (2015), 909-918. https://doi.org/10.22436/jnsa.008.06.02
  22. N. Hussain and P. Salimi, suzuki-wardowski type fixed point theorems for ${\alpha}$-GF-contractions, Taiwanese J. Math., 20 (2014), doi: 10.11650/tjm.18.2014.4462.
  23. N. Hussain, S. Al-Mezel and P. Salimi, Fixed points for ${\alpha}-{\psi}$-graphic contractions with application to integral equations, Abstr. Appl. Anal., (2013), Article 575869.
  24. J. Jachymski, The contraction principle for mappings on a metric space with a graph, Proc. Amer. Math. Soc., 1(136) (2008), 1359-1373.
  25. E. Karapinar and B. Samet, Generalized (${\alpha}-{\psi}$) contractive type mappings and related fixed point theorems with applications, Abstr. Appl. Anal., (2012), Article id:793486.
  26. E. Kryeyszig., Introductory Functional Analysis with Applications, John Wiley & Sons, New York, (Wiley Classics Library Edition) (1989).
  27. MA. Kutbi, M. Arshad and A. Hussain, On Modified ${\alpha}-{\eta}$-Contractive mappings, Abstr. Appl. Anal., (2014), Article ID 657858, 7 pages.
  28. MA. Kutbi, M. Arshad and A.Hussain, Fixed Point Results for Ciric type ${\alpha}-{\eta}$-GF-Contractions, journal of Computational Analysis and Applications 21(3) (2016), 466-481.
  29. G. Minak, A. Halvaci and I. Altun, Ciric type generalized F-contractions on complete metric spaces and fixed point results, Filomat, 28(6) (2014), 1143-1151. https://doi.org/10.2298/FIL1406143M
  30. SB. Nadler, Multivalued contraction mappings, Pac. J. Math., 30 (1969), 475-488. https://doi.org/10.2140/pjm.1969.30.475
  31. M. Nazam, M. Arshad and A. Hussain, Fixed Point Theorems For Chatterjea's type Contraction on Closed ball, Journal of Analysis and Number Theory. 5(1) (2017), 1-8. https://doi.org/10.18576/jant/050101
  32. H. Piri and P. Kumam, Some fixed point theorems concerning F-contraction in complete metric spaces, Fixed Point Theory Appl. (2014), 2014:210. https://doi.org/10.1186/1687-1812-2014-210
  33. M. Sgroi and C. Vetro, Multi-valued F-contractions and the solution of certain functional and integral equations, Filomat, 27(7) (2013), 1259-1268. https://doi.org/10.2298/FIL1307259S
  34. P. Salimi, A. Latif and N. Hussain, Modified ${\alpha}-{\psi}$-Contractive mappings with applications, Fixed Point Theory Appl. (2013), 2013:151. https://doi.org/10.1186/1687-1812-2013-151
  35. SU. Khan, M. Arshad and A. Hussain, Two new Types of fixed point theorems for F-contraction, Journal of Advanced Studies in Topology, 7(4) (2016), 251-260. https://doi.org/10.20454/jast.2016.1050
  36. NA. Secelean, Iterated function systems consisting of F-contractions, Fixed Point Theory Appl. (2013), Article ID 277 (2013). doi:10.1186/1687-1812-2013-277.
  37. A. Shoaib, M. Arshad and J. Ahmad, Fixed point results of locally cotractive mappings in ordered quasi-partial metric spaces, The Scienti c World Journal, 2013 (2013), Article ID 194897, 1-8.
  38. B. Samet, C. Vetro and P. Vetro, Fixed point theorems for ${\alpha}-{\psi}$-contractive type mappings, Nonlinear Anal. 75 (2012) 2154-2165. https://doi.org/10.1016/j.na.2011.10.014
  39. D. Wardowski, Fixed point theory of a new type of contractive mappings in complete metric spaces. Fixed PoinTheory Appl. (2012), Article ID 94.