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

The present study focuses on proving the existence of coincidence points for self-mappings satisfying a generalized contractive condition within the framework of convex metric spaces. The existence of common fixed points for weakly compatible self-mappings as well as Banach operator pairs under certain generalized contractions in a convex metric space is also established. MSC: 47H09; 47H10; 47H19; 54H25

The purpose of this paper is to present some fixed point and common fixed point theorems for almost generalized C-contractive mappings in an ordered complete metric space. Finally, two examples are given to support our results. MSC: 54H25; 47H10; 54E50

First we present a unified theory of connections on bundles necessary for the next studies. For a smooth manifold M , modeled on the Banach space B, we define the bundle of linear frames LM and we endow it with a differentiable structure. Bundle of sprays F M , the pullback of LM via the tangent bundle π : T M −→ M , is a natural bundle which provides us a rich environment to study the geometry of M. Afterward, despite of natural difficulties with Fréchet manifolds and even spaces, we generalize these results to a wide class of Fréchet manifolds, those which can be considered as projective limits of Banach manifolds. As an alternative approach we use pre-Finsler connections on F M and we show that our technique successfully solves ordinary differential equations on these manifolds. As some applications of our results we apply our method to enrich the geometry of two known Fréchet manifolds, i.e. jet of infinite sections and manifold of smooth maps, and we provide a suitable framework for further studies in these areas.