International Journal Of Nonlinear Analysis And Applications
Volume:3 Issue: 1, Summer - Autumn 2012

In this paper, we give some xed point theorems for '-weak contractive 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 xed point for a nite 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 re ne some known results in the current literature.

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

Let (X; d) be a complete metric space and let f; g: X 􀀀! X be two mappings which satisfy a (􀀀 ')-weak contraction condition or generalized (􀀀 ')-weak contraction condition. Then f and g have a unique common xed 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 ne spectrum of the Zweier matrix as an operator over the weighted sequence space `p(w); have been examined.

We show that every approximate solution of the Hosszu's functional equation f(x + y + xy) = f(x) + f(y) + f(xy) for any x; y 2 R; is an additive function and also we investigate the Hyers-Ulam stability of this equation in the following setting jf(x + y + xy) 􀀀 f(x) 􀀀 f(y) 􀀀 f(xy)j   + '(x; y) for any x; y 2 R and  > 0.

Let A = (an;k)n;k1 and B = (bn;k)n;k1 be two non-negative ma- trices. Denote by Lv;p;q;B(A), the supremum of those L, satisfying the following inequality: k Ax kv;B(q) L k x kv;B(p); where x  0 and x 2 lp(v;B) and also v = (vn)1 n=1 is an increasing, non-negative sequence of real numbers. In this paper, we obtain a Hardy-type formula for Lv;p;q;B(H), where H is the Hausdor matrix and 0 < q  p  1. Also for the case p = 1, we obtain kAkw;B(1), and for the case p  1, we obtain Lw;B(p)(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 L2; = L2 (R) = L2(R; jxj2 +1dx); >􀀀12.

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

We consider the coupled system F(x; y) = G(x; y) = 0, where F(x; y) = Xm1 k=0 Ak(y)xm1􀀀k and G(x; y) = Xm2 k=0 Bk(y)xm2􀀀k with entire functions Ak(y);Bk(y). We derive a priory estimates for the sums of the roots of the considered system and for the counting function of roots.