Generalize acute point and fixed point and convergence theorems (Study on Nonlinear Analysis and Convex Analysis)

In this paper we generalize the concept of acute point and we introduce some acute point type theorems that holds under the same assumptions as fixed point theorems. Furthermore we show that fixed point theorems are derived from acute point type theorems. Furthermore we introduce some convergence theorems that holds under the same assumptions on parameters as fixed point theorems

Regularly log-periodic functions and some applications

We prove a Tauberian theorem for the Laplace--Stieltjes transform and Karamata-type theorems in the framework of regularly log-periodic functions. As an application we determine the exact tail behavior of fixed points of certain type smoothing transforms

Fixed point theorems for α\alpha--contractive mappings of Meir--Keeler type and applications

In this paper, we introduce the notion of $\alpha$--contractive mapping of Meir--Keeler type in complete metric spaces and prove new theorems which assure the existence, uniqueness and iterative approximation of the fixed point for this type of contraction. The presented theorems extend, generalize and improve several existing results in literature. To validate our results, we establish the existence and uniqueness of solution to a class of third order two point boundary value problems

Some Ramsey theorems for finite nn-colorable and nn-chromatic graphs

Given a fixed integer $n$, we prove Ramsey-type theorems for the classes of all finite ordered $n$-colorable graphs, finite $n$-colorable graphs, finite ordered $n$-chromatic graphs, and finite $n$-chromatic graphs.Comment: 7 page

Unified multi-tupled fixed point theorems involving mixed monotone property in ordered metric spaces

In the present article, we introduce a unified notion of multi-tupled fixed points and utilize the same to prove some existence and uniqueness unified multi-tupled fixed point theorems for Boyd-Wong type nonlinear contractions satisfying generalized mixed monotone property in ordered metric spaces. Our results unify several classical and well-known n-tupled (including coupled, tripled and quadrupled ones) fixed point results existing in the literature.Comment: arXiv admin note: substantial text overlap with arXiv: 1601.0251