B_?(s)-Fixed Point Theorem Of F-compression Mapping In Generalized Metric Space

In this paper,under the background of complete b_?(s)-generalized metric space and on the basis of F contract on,we give three proofs of F-contraction fixed point theorems and their inferences in complete b_?(s)-generalized metric space respectively.In the first part,we introduce a new concept of generalized Khan type contraction and Khan type F contraction.On this basis,we define a new rational Khan F contraction type and provide the existence and uniqueness of a fixed point for this contraction by using the iterative approach.In the second part,we lead into the definition of ?-?-F rational contraction With the aid of triangular ?-admissible mapping,we generalize the fixed point theorem of?-?-F rational type contraction in the setting of rectangular b-metric space to complete b_?(s)-generalized metric space.In the third part of this paper,we define the concept of(?,?)-?-F rational contraction.With the aid of triangular(?,?)-admissible mappings,we prove the existence and uniqueness of a fixed point for this contractions under certain conditions in b_?(s)-metric space by using the iterative approach.Moreover,we generalize the obtained results which makes the theorem improved.