In this paper, we discuss the existence and uniqueness of fixed points for $G$-asymptotic contractions in metric spaces endowed with a graph. The result given here is a new version of Kirk's fixed point theorem for asymptotic contractions in metric spaces endowed with a graph. The given result here is a generalization of fixed point theorem for asymptotic contraction from metric s paces to metr...

At every point, a smooth plane curve can be approximated, to second order, by circle; this circle is called osculating. One may think of the osculating as passing through three infinitesimally close points curve. A vertex point at which hyper-osculates: it approximates third order. Equivalently, critical curvature function. Consider (necessarily non-closed) curve, free from vertices. The classi...

The contours =Λ(s) = 0 of the function which satisfies ζ(1− s) = Λ(s)ζ(s) cross the critical strip on lines which are almost horizontal and straight, and cut the critical line alternately at Gram points and points where ζ(s) is imaginary. The real part of ζ(s), when averaged in a modified manner, for fixed values of σ over the values on the “Gram lines”, satisfies a relation which extends a the...

Introduction: Hand and wrist stability are critical for optimal upper extremity function. Instability occurs when injury or a pathological condition alters balance, typically in the basketball players and handball players. Injury also can occur whenever the ligaments are subjected to tensile forces that exceed their physiological capacities. For example, thumb is stable in ext...

comnode classification within membrane residue curves (m-rcms) currently hinges on lyapunov’s theorem and therefore the computation of mathematically complex eigenvalues. this paper presents an alternative criterion for the classification of nodes within m-rcms based on the total membrane flux at node compositions. this paper demonstrates that for a system exhibiting simple permeation behaviour...

We establish an extension of Liouville’s classical representation theorem for solutions of the partial differential equation ∆u = 4 e2u and combine this result with methods from nonlinear elliptic PDE to construct holomorphic maps with prescribed critical points and specified boundary behaviour. For instance, we show that for every Blaschke sequence {zj} in the unit disk there is always a Blasc...

We provide fuzzy quasi-metric versions of a fixed point theorem ofGregori and Sapena for fuzzy contractive mappings in G-complete fuzzy metricspaces and apply the results to obtain fixed points for contractive mappingsin the domain of words.