We present some fixed point results for a single mapping and a pair of compatible mappings via auxiliary functions which satisfy a generalized weakly contractive condition in partially ordered complete $G$-metric spaces. Some examples are furnished to illustrate the useability of our main results. At the end, an application is presented to the study of exi...

This paper studies the proximal point algorithm for class of generalized variational inequalities. By using upper semicontinuity result establishing weakly univalent operators, we show that iterative sequence generated by is bounded, approaches to solution set initial problem, and each its accumulation points a provided bounded. We also give an example necessity boundedness.

let $g$ be a finite group‎. ‎a subgroup‎ ‎$h$ of $g$ is called an $mathcal h $ -subgroup in‎ ‎$g$ if $n_g (h)cap h^gleq h$ for all $gin‎ ‎g$. a subgroup $h$ of $g$ is called a weakly‎ $mathcal h^ast $-subgroup in $g$ if there exists a‎ ‎subgroup $k$ of $g$ such that $g=hk$ and $hcap‎ ‎k$ is an $mathcal h$-subgroup in $g$. we‎ ‎investigate the structure of the finite group $g$ under the‎ ‎assump...

A ring $R$ with identity is called ``clean'' if $~$for every element $ain R$, there exist an idempotent $e$ and a unit $u$ in $R$ such that $a=u+e$. Let $C(R)$ denote the center of a ring $R$ and $g(x)$ be a polynomial in $C(R)[x]$. An element $rin R$ is called ``g(x)-clean'' if $r=u+s$ where $g(s)=0$ and $u$ is a unit of $R$ and, $R$ is $g(x)$-clean if every element is $g(x)$-clean. In this pa...

The aim of this paper is to present some coincidence and common fixed point results for generalized (ψ, φ)-contractive mappings using partially weakly G-α-admissibility in the setup of G-metric space. As an application of our results, periodic points of weakly contractive mappings are obtained. We also derive certain new coincidence point and common fixed point theorems in partially ordered G-m...

In this paper, a variable coefficient generalized dispersive water-wave system which can model the propagation of the long weakly nonlinear and weakly dispersive surface waves of variable depth in shallow water is presented. With the aid of symbolic computation and using the generalized (G ′ G )-expansion method, the exact traveling wave solutions of this system are obtained. It is shown that t...

A minimal dynamical system (X,T ) is called quasi-Bohr if it is a nontrivial equicontinuous extension of a proximal system. We show that if (X,T ) is a minimal dynamical system which is not weakly mixing then some minimal proximal extension of (X, T ) admits a nontrivial quasi-Bohr factor. (In terms of Ellis groups the corresponding statement is: AG′ = G implies weak mixing.) The converse does ...

In this paper, we prove the existence and uniqueness of a common fixed point in symmetric generalized intuitionistic fuzzy metric spaces using property (E.A.) or CLRg property. We introduce new notion for pair mappings (f, g) on space called weakly commuting type (Jf ) R-weakly ).

a common fixed point result for weakly increasing mappings satisfying generalized contractive type of zhang in ordered metric spaces are derived.

In this paper, we study some common fixed point results for weakly compatible mapping satisfying Generalized Contraction Principle in G-metric space by using a control function.