Common Fixed Points Of G-B-K-C Type And Fixed Points Of (?)iri(?) Type On 2-metric Spaces

Banach fixed point theorem is one of the most fundamental and important theories in fixed point theory,and it has been widely used in mathematics and other areas.Banach fixed point theorem offers effective methods of solving the existence,uniqueness and iterative approximation of solutions in many fields.Many scholars continually extend and improve the Banach fixed point theorem.In the development of Banach fixed point theorems,there are some typical theo-rems,such as Geraghty type fixed point theorems,Kannan fixed point theorems,Chat-terjea fixed point theorems,Ciric fixed point theorems and some generalized or im-proved forms.Many authors improved and generalized Banach fixed point theorems in some metric spaces,like 2-metric space,cone metric space,b-metric space,G-metric space,multiplicative metric space,fuzzy metric space etc.,well developed the Banach fixed point theorems.In this paper,firstly,we discuss the unique existence of fixed points for two map-pings that Geraghty type condition on 2-metric spaces.Then combine Geraghty func-tions with Kannan contraction condition and Chatterjea contraction condition,which to obtain the existence theorems of unique common fixed points for two mappings and infinite mappings that Geraghty-Banach-Kannan type or Geraghty-Banach-Chatterjea type contractive conditions on 2-metric spaces.The obtained results are generalized results of the Geraghty-Banach-Kannan-Chatterjea type common fixed point theorem.Finally,we give a generalized quasi-contraction condition on a 2-metric space and Ciric type fixed point theorem and its more general form are obtained on the mapping orbitally complete 2-metric spaces.The obtained conclusions generalize and improve some known results,which made fixed point theorems have a better development and improvement in 2-matric spaces.