On some common fixed point theorems with PPF dependence in Banach spaces

Volume 5, Issue 3, pp 220--232 http://dx.doi.org/10.22436/jnsa.005.03.06

Download PDF

Download XML

• Export citations
  • CITATIONS & REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • ARTICLE CITATION
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)
  • REFERENCES
  • EndNote (.ENW)
  • Mendeley, JabRef (.BIB)
  • Papers, Zotero, Reference Manager, RefWorks (.RIS)

• 2386 Downloads
• 3987 Views

Authors

Bapurao C. Dhage - Kasubai, , Gurukul Colony, , Ahmedpur-413 515, Dist. Latur, Maharashtra, India.

Abstract

In this paper, some results concerning the existence of common fixed points, coincidence points and approximating fixed points with PPF dependence for the pairs of operators in Banach spaces satisfying a generalized contractive condition are proved. The novelty of the present work lies in the fact that the domain and the range spaces of the operators in questions are not same and all the results are obtained via constructive methods. Our results generalize and extend the fixed point theorems with PPF dependence of Bernfeld et al. [S. R. Bernfeld, V. Lakshmikatham and Y. M. Reddy, Applicable Anal. 6 (1977), 271-280] and Dhage [B. C. Dhage, Fixed point Theory, (to appear)] under more general contractive conditions.

Share and Cite

Keywords

• Banach space
• Fixed point theorem
• PPF dependence.

MSC

•  34K10
•  47H10

References

• [1] S. R. Bernfeld, V. Lakshmikatham, Y. M. Reddy , Fixed point theorems of operators with PPF dependence in Banach spaces, Applicable Anal. , 6 (1977), 271-280.


• [2] Lj. B. Ćirić, Generalized contraction and fixed point theorems, Publ. Inst Math , 12 (1971), 19-26.


• [3] Lj. B. Ćirić, A generalization of Banach's contraction principle, PAMS, 45 (1974), 267-273.


• [4] B. C. Dhage , Fixed point theorems with PPF dependence and functional differential equations, Fixed point Theory, 12 (2011), to appear


• [5] B. C. Dhage, Some basic random fixed point theorems with PPF dependence and functional random differential equations, Diff. Equ. Appl., 4 (2012), 181-195.


• [6] R. Kannan, Some results on fixed points II, Amer. Math. Monthly , 76 (1969), 405-408.


• [7] W. V. Petryshyn, T. E. Williamson, Strong and weak convergence of the sequences of successive approximations for quasi-nonexpansive mappings, J. Math. Anal. Appl. , 43 (1973), 459-497.


• [8] B. E. Rhoades, A comparison of various definitions of contractive mappings, Trans. AMS , 226 (1977), 257-290.