In the present paper, we introduce the concept of generalized multivalued F -contraction mappings and give a fixed point result, which is a proper generalization of some multivalued fixed point theorems including Nadler's.

The aim of this paper is to prove the existence and uniqueness of fixed point for (j-f)-weak contraction mappings and (y−f)-weak contraction mappings in a Complete and Hausdorff generalized metric space.

We improve Park and Bae's common fixed point theorem which is a generalization of Meir and Keeler's fixed point theorem. We extend Kannan's fixed point theorem to a common fixed point theorem of two commuting maps. Also, using the notion of biased mappings, we prove another common fixed point theorem.  

Hadamard (or CompleteCAT (0)) spaces are Complete, non-positive curvature, metric spaces. Here, we prove a nonlinear ergodic theorem for continuous non-expansive semigroup in these spaces as well as a strong convergence theorem for the commutative case. Our results extend the standard non-linear ergodic theorems for non-expansive maps on real Hilbert spaces, to non-expansive maps on Hadamard spaces, which include for example (possibly infinite-dimensional) Complete simply connected Riemannian manifolds with non-positive sectional curvature.

In this article, we will study the existence and uniqueness of optimal common fixed points for self-mappings in metric spaces with w-distance. We obtain generalizations of the Kocev and Rako\v{c}evi\'{c} fixed point theorems. The obtained results do not require the continuity or the condition $(C;k)$ of maps,  but require the weaker condition $(W)$. We also improve some of our results when the metric space is equipped with a w$_0$-distance. In this way, we get new existence results for non-cyclic quasi-contraction mappings of the Fisher type.

In this paper, we define the concept of compatible and weakly compatible mappings in b-metric spaces and inspired by the Ciric and et. al method, we produce appropriate conditions for given the unique common fixed point for a family of the even number of self-maps with together another two self-maps in a Complete b-metric spaces. Also, we generalize this common fixed point theorem for a sequence with together an even numbers of self-maps in Complete b-metric spaces.

In this paper, we define rational type Geraghty tower contraction mapping and prove the existence of such finite and infinite rational Geraghty tower theorem(s) in Complete metric spaces. The results we establish in this paper extend, improve, generalise and unify some existing results in the literature.