Fixed point theorems in convex metric spaces

Abstract

In this paper, we study some fixed point theorems for self-mappings satisfying certain contraction principles on a convex complete metric space. In addition, we investigate some common fixed point theorems for a Banach operator pair under certain generalized contractions on a convex complete metric space. Finally, we also improve and extend some recent results. MSC: 47H09; 47H10; 47H19; 54H25

Fixed point theorems for generalized contraction mappings on b-rectangular metric spaces

“…Moosaei in [15] used Krasnoselskii iteration to develop fixed point theorems for generalized contractions on convex metric spaces. It is easily seen that we can use Picard instead of Krasnoselkii sequences in metric spaces.…”

“…It is easily seen that we can use Picard instead of Krasnoselkii sequences in metric spaces. In this section, our aim is to extend the results of Moosaei [15] for generalized contraction mappings from metric spaces to b-rectangular metric spaces. Also, we extend and develop the fixed point results of Aage [1] from cone metric spaces to b-g.m.s.…”

“…Moosaei, Azizi, Asadi and Wang generalized the results of Karapinar as follows In [15], Moosaei used Krasnoselskii's iteration defined in convex metric spaces, for the following mappings, that satisfy…”

Extension of Some Common Fixed Point Theorems

“…Takahashi [11], [12] introduced the notion of convexity in metric spaces, and discussed some fixed point theorems for nonexpansive mappings in such convex metric spaces. Mohammad Moosaei [13]- [15] obtained some fixed point theorems for self-mappings satisfying certain contraction principles on a convex complete metric space. In [16], a hybrid iteration method was employed and the strong convergence of the iteration scheme to a fixed point of nonself nonexpansive mapping was derived in Banach spaces.…”

Extension of Some Common Fixed Point Theorems

“…Mohammad Moosaei [12] has studied some fixed point theorems for selfmappings satisfying certain contraction principles on a convex complete metric space. Also, he has investigated some common fixed point theorems for a Banach operator pair under certain generalized contractions on a complete metric space.…”