Common fixed points of single-valued and multivalued maps

We define a new property which contains the property (EA) for a hybrid pair of single- and multivalued maps and give some new common fixed point theorems under hybrid contractive conditions. Our results extend previous ones. As an application, we give a partial answer to the problem raised by Singh and Mishra.

[1]  S.V.R. Naidu.  Fixed point theorems for a broad class of multimaps , 2003 .

[2]  William A. Kirk,et al.  A generalization of Caristi’s theorem with applications to nonlinear mapping theory , 1977 .

[3]  William A. Kirk,et al.  Set-valued contractions and fixed points , 2003 .

[4]  Teck-Cheong Lim,et al.  On characterizations of Meir-Keeler contractive maps , 2001 .

[5]  Jong Sook Bae,et al.  Fixed point theorems for weakly contractive multivalued maps , 2003 .

[6]  J. S. W. Wong,et al.  On nonlinear contractions , 1969 .

[7]  D. El Moutawakil,et al.  Some new common fixed point theorems under strict contractive conditions , 2002 .

[8]  Yicheng Liu,et al.  Schaefer type theorem and periodic solutions of evolution equations , 2006 .

[9]  Marlène Frigon.  Fixed point results for generalized contractions in gauge spaces and applications , 2000 .

[10]  Tomonari Suzuki,et al.  Generalized Caristi's fixed point theorems by Bae and others , 2005 .

[11]  B. Rhoades,et al.  A comparison of various definitions of contractive mappings , 1977 .

[12]  K. Deimling.  Fixed Point Theory , 2008 .

[13]  Tayyab Kamran,et al.  Coincidence and fixed points for hybrid strict contractions , 2004 .

[14]  Wataru Takahashi,et al.  Fixed point theorems and characterizations of metric completeness , 1996 .

[15]  Paula Oliveira.  Two results on fixed points , 2001 .

[16]  Troy L. Hicks,et al.  FIXED POINTS AND CONTINUITY FOR MULTIVALUED MAPPINGS , 1992 .

[17]  S. N. Mishra,et al.  Coincidences and Fixed Points of Nonself Hybrid Contractions , 2001 .

[18]  Jeong Sheok Ume,et al.  Multi-valued non-self-mappings on convex metric spaces , 2005 .

[19]  Vasile I. Istrăţescu,et al.  Fixed point theory : an introduction , 1981 .

[20]  Mohammad Imdad,et al.  Some common fixed point theorems for mappings and multi-valued mappings , 1998 .

[21]  Teck-Cheong Lim.  A fixed point theorem for weakly inward multivalued contractions , 2000 .

[22]  Naseer Shahzad,et al.  COINCIDENCE POINTS AND R-SUBWEAKLY COMMUTING MULTIVALUED MAPS , 2003 .