Coincidence and Fixed Point Theorems for Multivalued and Singlevalued Mappings
Keywords:
Coincidence Point, Fixed Point, Control Function, Weak Contraction.Abstract
In this paper we establish results on the existence of coincidence and fixed points for weakly contractive mappings.Downloads
Metrics
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2015 U. C. Gairola, Ram Krishan
This work is licensed under a Creative Commons Attribution 4.0 International License.
References
M. Abbas and D. Dori´c, A common End point theorem for set-valued generalized (ψ, φ)weak contraction, Fixed Point Theory Appl., 2010 (2010), Article ID 509658, 1–8.
Ya. I. Alber and S. Guerre-Delabriere, Principles of weakly contractive maps in Hilbert spaces, in: I. Goldberg, Yu. Lyubich , (eds.), New Results in Operator Theory, in: Advances and Appl., 98, Birkh¨auser, Basel, (1997), 7–22.
B. S. Choudhury, P. Konar, B. E. Rhoades and N. Metiya, Fixed point theorems for generalized weakly contractive mappings, Nonlinear Anal., 74(6) (2011), 2116–2126.
B. S. Choudhury and N. Metiya, Multi-valued and single-valued fixed point results in partially ordered metric spaces, Arab J. Math. Sci., 17 (2011), 135–151.
Lj. B. Ciri´c, ´ Fixed points for generalized multi-valued contractions, Mat. Vasnik, 9 (24) (1972), 265–272.
B. Damjanovi´c and D. Dori´c, Multi-valued generalizations of the Kannan fixed point theorem, Filomat 25 (1) (2011), 125–131.
D. Delbosco, Un'estensione di un teorema sul puto fisso di. S. Reich., Rend. Sem. Mat. Univers. Torino, 35 (1976–77), 233-238.
P. N. Dutta and B. S. Choudhury, A generalization of contraction principle in metric spaces, Fixed Point Theory Appl., (2008), Article ID 406368, 1–8.
O. Hadˇzi´c and Lj. Gaji´c, Coincidence points for set-valued mappings in convex metric spaces, Univ. Novom Sadu Zb. Rad. Prirod- Mat. Fak. Ser., 16 (1986), 13–25.
S. Itoh and W. Takahashi, Single-valued mappings, multi-valued mappings and fixed point theorems, J. Math. Anal. Appl., 59 (1977), 514–521.
G. Jungck, Common fixed points for non-continuous non-self maps on non-metric spaces, Far East J. Math. Sci., 4 (1996), 199–215.
G. Jungck and B. E. Rhoades, Fixed point for set-valued functions without continuity, Indian J. Pure Appl. Math., 29(3) (1998), 227–238.
H. Kaneko and S. Sessa, Fixed point theorems for compatible multi-valued and singlevalued mappings, Internat. J. Math. Math. Sci. 12(2) (1989), 257–262.
M. S. Khan, Common fixed point theorems for multi-valued mappings, Pacific J. Math., 95(2) (1981), 337–347.
M. S. Khan, M. Swaleh and S. Sessa, Fixed point theorems by altering distances between the points, Bull. Austral. Math. Soc., 30 (1984), 1–9.
S. B. Nadler, Multi-valued contraction mappings, Pacific J. Math., 30(2) (1969), 475– 487.
R. P. Pant, Common fixed point theorems for contractive maps, J. Math. Anal. Appl., 226 (1998), 251–258.
B. E. Rhoades, A comparison of various definitions of contractive mappings, Trans. Amer. Math. Soc., 226 (1977), 257–290.
B. E. Rhoades, Some theorems on weakly contractive maps, Nonlinear Anal., 47 (2001), 2683–2693.
S. L. Singh and C. Kulshrestha, Coincidence theorems in metric spaces, Indian J. Phy. Natur. Sci., 2 (1982), 19–22.
S. L. Singh and S. N. Mishra, Coincidences and fixed points of non-self hybrid contractions, J. Math. Anal. Appl., 256 (2001), 486–497.
S. L. Singh, K. S. Ha and Y. J. Cho, Coincidence and fixed points of nonlinear hybrid contractions, Internat. J. Math. Math. Sci., 12(2) (1989), 247–256.
F. Skof, Teorma di punti fisso per applicazioni negli spazi metrici, Atti. Acad. Sci. Torino, 111 (1977), 323–329.