recently, zhang and song [q. zhang, y. song, fixed point theory forgeneralized $varphi$-weak contractions,appl. math. lett. 22(2009) 75-78] proved a common fixed point theorem for two mapssatisfying generalized $varphi$-weak contractions. in this paper, we prove a common fixed point theorem fora family of compatible maps. in fact, a new generalization of zhangand song's theorem is given.

Recently, Zhang and Song [Q. Zhang, Y. Song, Fixed point theory forgeneralized $varphi$-weak contractions,Appl. Math. Lett. 22(2009) 75-78] proved a common fixed point theorem for two mapssatisfying generalized $varphi$-weak contractions. In this paper, we prove a common fixed point theorem fora family of compatible maps. In fact, a new generalization of Zhangand Song's theorem is given.

For a monochrome layer $x$ of opacity $0\le o_x\le1 $ placed on another monochrome layer of opacity 1, the result given by the standard formula is $$\small\Pi\left({\bf C}_\varphi\right)=1+\sum_{n=1}^2\left(2-n-(-1)^no_{\chi(\varphi+1)}\right)\left(\chi(n+\varphi-1)-o_{\chi(n+\varphi-1)}\right),$$ the formula being of course explained in detail in this paper. We will eventually deduce a very si...

For a fixed graph $H$, the reconfiguration problem for $H$-colourings (i.e. homomorphisms to $H$) asks: given a graph $G$ and two $H$-colourings $\varphi$ and $\psi$ of $G$, does there exist a sequence $f_0,\dots,f_m$ of $H$-colourings such that $f_0=\varphi$, $f_m=\psi$ and $f_i(u)f_{i+1}(v)\in E(H)$ for every $0\leq i<m$ and $uv\in E(G)$? If the graph $G$ is loop-free, then this is the equiva...

In the present paper, the notion of generalized $(r;g,s,m,varphi)$-preinvex function is applied to establish some new generalizations of Ostrowski type integral inequalities via Caputo $k$-fractional derivatives. At the end, some applications to special means are given.

(3) JC'C' and (3) JHNHα couplings are related to the intervening backbone torsion angle ${\varphi }$ by standard Karplus equations. Although these couplings are known to be affected by parameters other than ${\varphi }$, including H-bonding, valence angles and residue type, experimental results and quantum calculations indicate that the impact of these latter parameters is typically very small....

Emulsions of water in as-recovered native crude oils of diverse geographical origin evidently possess some common morphological features. At low volume fractions varphi of water, the viscosity behavior of emulsions is governed by the presence of flocculated clusters of water droplets, whereas characteristic tight gels, composed of visually monodisperse small droplets, are responsible for the vi...

For a fixed nonnegative integer $m$, an analytic map $\varphi$ and function $\psi$, the generalized integration operator $I^{(m)}_{\varphi,\psi}$ is defined by \[ I^{(m)}_{\varphi,\psi} f(z) = \int_0^z f^{(m)}(\varphi(\zeta)) \psi(\zeta) \, d\zeta \] for $X$-valued $f$, where $X$ Banach space. Some estimates norm of $I^{(m)}_{\varphi,\psi} \colon wA^p_{\alpha}(X) \to A^p_{\alpha}(X)$ are obtain...

We prove higher integrability of the spatial gradient weak solutions to parabolic systems with $\phi$-growth, where $\varphi=\varphi(t)$ is a general Orlicz function. The need be neither degenerate nor singular. Our result generalized version one J. Kinnunen and Lewis [Duke Math. 102 (2000), no. 2, 253--271] for $p$-Laplace systems.

by means of a kind of new idea, we consider  the $(in,ivq)$-fuzzy$h$-ideals of a hemiring.  first, the concepts of $(in,ivq)$-fuzzyleft(right) $h$-ideals of a hemiring are provided and some relatedproperties are investigated. then, a kind  of quotient hemiring  ofa hemiring by an $(in,ivq)$-fuzzy $h$-ideal is presented andstudied. moreover, the notions of generalized $varphi$-compatible$(in,ivq...