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The weak convergence of the iterative generated by $J(u_{n+1}-u_n)=\tau (F{u}_n-J{u}_n)$, $n\ge 0$, $(0<\tau =min\{1,\frac{1}{\lambda }\})$ to a coincidence point of the mappings $F,J:V\to V^{☆}$ is investigated, where $V$ is a real reflexive Banach space and $V^{☆}$ its dual (assuming that $V^{☆}$ is strictly convex). The basic assumptions are that $J$ is the duality mapping, $J-F$ is demiclosed at $0$, coercive, potential and bounded and that there exists a non-negative real valued function $r(u,\eta )$ such that $$\underset{u,\eta \in V}{sup}\left\{r(u,\eta )\right\}=\lambda <\infty$$ $${r(u,\eta )\parallel J(u-\eta )\parallel }_{V^{☆}}\ge {\parallel (J-F)\left(u\right)-(J-F)\left(\eta \right)\parallel }_{V^{☆}},\forall u,\eta \in V.$$ Furthermore, the case when $V$ is a Hilbert space is given. An application of our results to...

In this paper we study some extended results of the Hadamard product set for several simple monic sets of polynomials of several complex variables in hyperspherical regions, then we obtain the effectiveness conditions for this Hadamard product in hyperspherical regions.

In this paper we study the existence of solution of a nonlinear integral equation of (mixed type) Volterra-Fredholm type. As an application we prove the existence of solution of an initial value problem of fractional order in the space of Lebesgue integrable functions on the interval $[0,1]$.