In this paper, we introduce the concept of contractive pair maps and give some necessary sufficient conditions for existence uniqueness best proximity points such pairs. our approach, have been weakened. An application has presented to demonstrate usability results. Also, cyclic ?-contraction asymptotic convergence theorems on point mappings. The results extend, generalize improve known from th...

During repetitive contractions, muscular work has been shown to exhibit complex relationships with muscle strain length, cycle frequency, and muscle shortening velocity. Those complex relationships make it difficult to predict muscular performance for any specific set of movement parameters. We hypothesized that the relationship of impulse with cyclic velocity (the product of shortening velocit...

Therapies that mitigate the fibrotic process may be able to slow progressive loss of function in many lung diseases. Because cyclic adenosine monophosphate is known to regulate fibroblasts, the current study was designed to evaluate the activity of selective phosphodiesterase (PDE) inhibitors on two in vitro fibroblast responses: chemotaxis and contraction of three-dimensional collagen gels. Se...

Abstract In this paper, we introduce the notions of proximal Berinde g -cyclic contractions two non-self-mappings and -contractions, called contraction first second kind. Coincidence best proximity point theorems for these types mappings in a metric space are presented. Some examples illustrating our main results also given. Our extend generalize many existing literature.

Let $T=\bigl(\begin{smallmatrix}A&0\U\&B\end{smallmatrix}\bigr)$ be a formal triangular matrix ring, where $A$ and $B$ are rings $U$ is $(B, A)$-bimodule. We prove: (1) If $U\_{A}$ ${B}U$ have finite flat dimensions, then left $T$-module $\bigl(\begin{smallmatrix}M\_1\ M\_2\end{smallmatrix}\bigr){\varphi^{M}}$ Ding projective if only $M\_1$ $M\_2/{\operatorname{im}(\varphi^{M})}$ the morphism $...

Abstract Let $\varphi $ be Euler’s function and fix an integer $k\ge 0$ . We show that for every initial value $x_1\ge 1$ , the sequence of positive integers $(x_n)_{n\ge 1}$ defined by $x_{n+1}=\varphi (x_n)+k$ all $n\ge is eventually periodic. Similarly, values $x_1,x_2\ge $x_{n+2}=\varphi (x_{n+1})+\varphi periodic, provided k even.