In this paper, we give some fixed point theorems for $varphi$-weak contraction type mappings on complete G-metric space, which was given by Zaed and Sims [1]. Also a homotopy result is given.

In this paper, we give some fixed point theorems for $varphi$-weak contraction type mappings on complete G-metric space, which was given by Zaed and Sims [1]. Also a homotopy result is given.

In this paper, we introduce and study a new iterative scheme to approximate a common fixed point for a finite family of generalized asymptotically quasi-nonexpansive nonself-mappings in Banach spaces. Several strong and weak convergence theorems of the proposed iteration are established. The main results obtained in this paper generalize and refine some known results in the current literature.

In this paper we obtain a unique common fixed point theorem for six weakly compatible mappings in G-metric spaces.

Let $(X, d)$ be a complete metric space and let $f,g : X to X$ be two mappings which satisfy a ($psi$-$varphi$)-weak contraction condition or generalized ($psi$-$varphi$)-weak contraction condition. Then $f$ and $g$ have a unique common fixed point. Our results extend previous results given by Ciric (1971), Rhoades (2001), Branciari (2002), Rhoades (2003), Abbas and Ali Khan (2009), Zhang and Song (2009) and Moradi at. el. (2011).

In the present paper, the fine spectrum of the Zweier matrix as an operator over the weighted sequence space $ell_p(w)$, has been examined.

We show that every approximate solution of the Hosszu's functional equation$$f(x + y + xy) = f(x) + f(y) + f(xy) text{for any} x, yin mathbb{R},$$is an additive function and also we investigate the Hyers-Ulam stability of this equation in the following setting$$|f(x + y + xy) - f(x) - f(y) - f(xy)|leqdelta + varphi(x; y)$$for any $x, yin mathbb{R}$ and $delta > 0$.

Let $A=(a_{n,k})_{n,kgeq1}$ and $B=(b_{n,k})_{n,kgeq1}$ be two non-negative matrices. Denote by $L_{v,p,q,B}(A)$, the supremum of those $L$, satisfying the following inequality:$$|Ax|_{v,B(q)}geq L|x|_{v,B(p)},$$where $xgeq 0$ and $x in l_p(v,B)$ and also$v = (v_n)_{n=1}^infty$ is an increasing, non-negative sequence of real numbers. In this paper, we obtain a Hardy-type formula for $L_{v,p,q,B}(H_mu)$, where $H_mu$ is the Hausdorff matrix and $0 < q leq p leq1$. Also for the case $p = 1$, we obtain $|Ax|_{v,B(1)}$, and for the case $pgeq 1$, we obtain $L_{v,p,q,B}(A)$.

In this paper, using a generalized Dunkl translation operator, we obtain an analog of Titchmarsh's Theorem for the Dunkl transform for functions satisfying the Lipschitz-Dunkl condition in $mathrm{L}_{2,alpha}=mathrm{L}_{alpha}^{2}(mathbb{R})=mathrm{L}^{2}(mathbb{R}, |x|^{2alpha+1}dx), alpha>frac{-1}{2}$.

In this paper, the solution of the evolutionary fourth-order in space, Sivashinsky equation is obtained by means of homotopy perturbation method (textbf{HPM}). The results reveal that the method is very effective, convenient and quite accurate to systems of nonlinear partial differential equations.

We consider the coupled system $F(x,y)=G(x,y)=0$, where$$F(x, y)=sum_{k=0}^{m_1} A_k(y)x^{m_1-k} quad text{ and }quad G(x, y)=sum_{k=0}^{m_2} B_k(y)x^{m_2-k}$$with entire functions $A_k(y), B_k(y)$. We derive a priory estimate for the sums of the roots of the considered system and for the counting function of roots.