On α-ψ-Meir-Keeler contractive mappings

In this paper, we introduce the notion of α-ψ-Meir-Keeler contractive mappings via a triangular α-admissible mapping. We discuss the existence and uniqueness of a fixed point of such a mapping in the setting of complete metric spaces. We state a number of examples to illustrate our results.MSC:46N40, 47H10, 54H25, 46T99.

[1]  Hassen Aydi,et al.  Common fixed points of generalized contractions on partial metric spaces and an application , 2011, Appl. Math. Comput..

[2]  Simeon Reich,et al.  Some Remarks Concerning Contraction Mappings , 1971, Canadian Mathematical Bulletin.

[3]  Bessem Samet,et al.  Fixed point theorems for α–ψ-contractive type mappings , 2012 .

[4]  Erdal Karapinar,et al.  weak φ-contraction on partial metric spaces and existence of fixed points in partially ordered sets , 2011 .

[5]  Erdal Karapinar,et al.  Fixed point theorems for operators on partial metric spaces , 2011, Appl. Math. Lett..

[6]  Erdal Karapınar,et al.  A NOTE ON COMMON FIXED POINT THEOREMS IN PARTIAL METRIC SPACES , 2011 .

[7]  D. R. Smart Fixed Point Theorems , 1974 .

[8]  R. Kannan,et al.  Some Results on Fixed Points—II , 1969 .

[9]  Erdal Karapinar,et al.  Corrigendum to "Fixed point theory for cyclic weak ϕ-contraction" [Appl. Math. Letters 24 (6) (2011) 822-825] , 2012, Appl. Math. Lett..

[10]  Erdal Karapınar,et al.  Fixed Point Theory for Cyclic Generalized Weak -Contraction on Partial Metric Spaces , 2012 .

[11]  Bessem Samet,et al.  Generalized - Contractive Type Mappings and Related Fixed Point Theorems with Applications , 2012 .

[12]  William A. Kirk,et al.  FIXED POINTS FOR MAPPINGS SATISFYING CYCLICAL CONTRACTIVE CONDITIONS , 2008 .

[13]  Erdal Karapinar,et al.  Generalizations of Caristi Kirk's Theorem on Partial Metric Spaces , 2011 .

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

[15]  Erdal Karapınar,et al.  Fixed Point Theorems in Cone Banach Spaces , 2009 .

[16]  Erdal Karapınar Some Nonunique Fixed Point Theorems of Ćirić Type on Cone Metric Spaces , 2010 .

[17]  G. E. Hardy,et al.  A Generalization of a Fixed Point Theorem of Reich , 1973, Canadian Mathematical Bulletin.

[18]  Erdal Karapinar,et al.  Some Common Fixed Point Theorems in Partial Metric Spaces , 2011, J. Appl. Math..

[19]  Erdal Karapinar,et al.  Fixed point theory for cyclic weak ϕ-contraction , 2011, Appl. Math. Lett..

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

[21]  M. Edelstein On Fixed and Periodic Points Under Contractive Mappings , 1962 .

[22]  Some Unique Fixed Point Theorems in Multiplicative Metric Spaces , 2014, 1410.3384.

[23]  V. Berinde,et al.  General constructive fixed point theorems for Ćirić-type almost contractions in metric spaces , 2008 .

[24]  S. K. Chatterjea Fixed Point Theorems For A Sequence Of Mappings With Contractive Iterates , 1972 .