Wojtaszewski, Jørgen F. P., Jan Lynge,Allan B. Jakobsen, Laurie J. Goodyear, and Erik A. Richter. Differential regulation of MAP kinase by contraction and insulin in skeletal muscle: metabolic implications. Am. J. Physiol. 277 (Endocrinol. Metab. 40): E724–E732, 1999.—We have investigated the activation of the extracellular signal-regulated kinases (ERK1 and ERK2) by muscle contraction and insu...

In the year 2014, Almeida et al. introduced a new class of mappings, namely, contractions Geraghty type. Additionally, in 2021, Beg concept generalized F-proximal contraction first kind and second kind, respectively. After developing these concepts, authors mainly studied best proximity points for classes mappings. this short note, we prove that problem existence said proximal is equivalent to ...

Given a graph G on n vertices and two integers k d, the Contraction(vc) problem asks whether one can contract at most edges to reduce vertex cover number of by least d. Recently, Lima et al. [JCSS 2021] proved that admits an XP algorithm running in time f(d)⋅nO(d). They asked this is FPT under parameterization. In article, we prove that: (i) W[1]-hard parameterized k+d. Moreover, unless ETH fai...

The focus of this research article is to investigate the notion fuzzy extended hexagonal b-metric spaces as a technique broadening rectangular and well derive Banach fixed point theorem several novel theorems with certain contraction mappings. analog inequality in specified follows utilizing function b(c,d): mhc,d,t+s+u+v+w?mhc,e,tb(c,d)?mhe,f,sb(c,d)?mhf,g,ub(c,d)?mhg,k,vb(c,d)?mhk,d,wb(c,d) f...

Abstract In this paper, we study a functional equation for generating functions of the form $$f(z) = g(z) \sum _{i=1}^M p_i f(\alpha _i(z)) + K(z)$$ f ( z ) = g ∑ i <...

We define two polynomials f(G) and /*(G) for a graph G by a recursive formula with respect to deformation of graphs. Analyzing their various properties, we shall discuss when two graphs have the same polynomials. Introduction. Our graphs are finite, undirected ones with or without self-loops and multiple edges. As elementary deformations of graphs, we have the deletion and the contraction of ed...

We introduce the concept of (EA) property and occasional w-compatibility for hybrid pair F : X × X → 2 (X) and f : X → X. We also introduce common (EA) property for two hybrid pairs F, G : X → 2 (X) and f, g : X → X. We establish some common coupled fixed point theorems for two hybrid pairs of mappings under φ-ψ contraction on noncomplete metric spaces. An example is also given to validate our ...

Proposition A–1. Suppose that F : R → R is a contraction mapping such that ‖F (x)− F (y)‖ ≤ λ ‖x− y‖ where λ ∈ [0, 1). Consider a closed convex set A ⊆ R and let π denote projection onto A; i.e., π(x) = argmin{‖x− y‖ : y ∈ A}. Let x = (x∗1, . . . , x∗d) denote the unique fixed point of F and suppose x ∈ A. Consider stochastic processes {Xk = (X 1 , . . . ,X d ) : k = 0, 1, 2, . . . } and ǫ = {(...

Let H be a real Hilbert space. Consider on H a nonexpansive family T = {T(t) : 0 ≤ t < ∞} with a common fixed point, a contraction f with the coefficient 0 0. Assume that 0 < γ < γ̄ /α and that S = {S (t) : 0 ≤ t < ∞} is a family of nonexpansive self-mappings on H such that F(T ) ⊆ F(S) and T has prop...