in this paper, we introduce the (g-$psi$) contraction in a metric space by using a graph.let $f,t$ be two multivalued mappings on $x.$ among other things, we obtain a common fixedpoint of the mappings $f,t$ in the metric space $x$ endowed with a graph $g.$

The existence and uniqueness of a periodic solution of the system of differential equations d dt x(t) = A(t)x(t − ) are proved. In particular the Krasnoselskii’s fixed point theorem and the contraction mapping principle are used in the analysis. In addition, the notion of fundamental matrix solution coupled with Floquet theory is also employed.  

This paper deals with a nonlinear fractional differential equation with integral boundary condition of the following form: { D t x(t) = f(t, x(t), D β t x(t)), t ∈ (0, 1), x(0) = 0, x(1) = ∫ 1 0 g(s)x(s)ds, where 1 < α ≤ 2, 0 < β < 1. Our results are based on the Schauder fixed point theorem and the Banach contraction principle. Keywords—Fractional differential equation; Integral boundary condi...

The main objective of this work is to introduce a new type non-linear contraction via C-class functions by using ?-admissible mapping. Our results extend and generalize the very recent Karapinar Sadarangani (2015. RACSAM. [37]). Illustrative examples are given support our findings. We have shown that satisfy periodic fixed point after modifying contraction. Next, we findings from self-mapping T...

It has been established quite recently [1], that a contraction T , having finite defects (rank (I − T T ), rank (I − TT ) < ∞) and the spectrum σ(T ) not filling in the closed unit disk D, is similar to a normal operator if and only if C1(T ) = sup λ6∈σ(T ) ||(T − λ)|| · dist(λ, σ(T )) < ∞. It was shown later [9], that the “only if” part of the assertion is no longer true if T is not a contract...

we investigated contraction to noradrenaline (na) and kc1 and sensitivity of na at the level of larger vessels (thoracic aorta and vena cava; left renal artery and left renal vein; lateral saphenous artery and lateral saphenous vein and finally central ear artery and marginal ear vein) in a model devised to mimic heart failure. the model presented here is the rabbit coronary ligation model in w...

BACKGROUND In pulmonary arterial hypertension (PAH) a prolonged time interval between pulmonary valve closure and tricuspid valve opening is found. This period is interpreted as prolonged right ventricular (RV) relaxation, and thus a reflection of diastolic dysfunction. This concept recently has been questioned, since it was shown that RV contraction continues after pulmonary valve closure caus...

We study a cyclic proof system C over regular expression types, inspired by linear logic and non-wellfounded theory. Proofs in can be seen as strongly typed goto programs. show that they denote computable total functions we analyse the relative strength of Gödel’s T. In general case, prove two systems capture same on natural numbers. affine i.e., when contraction is removed, precisely primitive...