Fixed point theorems for contraction mappings in modular metric spaces

In this article, we study and prove the new existence theorems of fixed points for contraction mappings in modular metric spaces.AMS: 47H09; 47H10.

[1]  中野 秀五郎,et al.  Modulared semi-ordered linear spaces , 1950 .

[2]  S. Yamamuro.  ON CONJUGATE SPACES OF NAKANO SPACES , 1959 .

[3]  Abdolrahman Razani,et al.  Fixed Points of Nonlinear and Asymptotic Contractions in the Modular Space , 2007 .

[4]  W. Luxemburg,et al.  BANACH FUNCTION SPACES , 2011 .

[5]  G. Jungck.  Compatible mappings and common fixed points , 1986 .

[6]  Abdolrahman Razani,et al.  Two Fixed-Point Theorems for Mappings Satisfying a General Contractive Condition of Integral Type in the Modular Space , 2010, Int. J. Math. Math. Sci..

[7]  Poom Kumam,et al.  Gregus type fixed points for a tangential multi-valued mappings satisfying contractive conditions of integral type , 2011 .

[8]  Mohamed A. Khamsi,et al.  Uniformly Lipschitzian mappings in modular function spaces , 2001 .

[9]  Poom Kumam,et al.  Coincidence and common fixed points for hybrid strict contractions without the weakly commuting condition , 2009, Appl. Math. Lett..

[10]  S. Banach.  Sur les opérations dans les ensembles abstraits et leur application aux équations intégrales , 1922 .

[11]  Poom Kumam,et al.  Common fixed point theorems for generalized JH-operator classes and invariant approximations , 2011 .

[12]  Poom Kumam,et al.  Fixed points of asymptotic pointwise contractions in modular spaces , 2011, Appl. Math. Lett..

[13]  J. Musielak,et al.  On modular spaces , 1959 .

[14]  T. Shimogaki,et al.  ON F-NORMS OF QUASI-MODULAR SPACES , 1961 .

[15]  Poom Kumam,et al.  Fixed Point and Common Fixed Point Theorems for Generalized Weak Contraction Mappings of Integral Type in Modular Spaces , 2011, Int. J. Math. Math. Sci..

[16]  Vyacheslav V. Chistyakov,et al.  Metric modulars and their application , 2006 .

[17]  B. Rhoades,et al.  Some theorems on weakly contractive maps , 2001 .

[18]  Poom Kumam,et al.  On uniform opial condition, Uniform Kadec-Klee property in modular spaces and application to fixed point theory , 2005 .

[19]  Vyacheslav V. Chistyakov,et al.  Modular metric spaces, I: Basic concepts , 2010 .

[20]  Yeol Je Cho,et al.  Common fixed point theorems for c-distance in ordered cone metric spaces , 2011, Comput. Math. Appl..

[21]  Mohamed A. Khamsi,et al.  Quasicontraction Mappings in Modular Spaces without Δ2-Condition , 2008 .

[22]  Chistyakov Vyacheslav,et al.  Modular metric spaces generated by F-modulars , 2008 .

[23]  Poom Kumam,et al.  FIXED POINT THEOREMS FOR NONEXPANSIVE MAPPINGS IN MODULAR SPACES , 2004 .

[24]  Poom Kumam,et al.  Weak condition for generalized multi-valued (f, alpha, beta)-weak contraction mappings , 2011, Appl. Math. Lett..