We introduce an iterative scheme for finding a common element of the solution set of a maximal monotone operator and the solution set of the variational inequality problem for an inverse strongly-monotone operator in a uniformly smooth and uniformly convex Banach space, and then we prove weak and strong convergence theorems by using the notion of generalized projection. The result presented in ...

Let C be a bounded closed convex subset of a uniformly convex Banach space X and let T be an asymptotically nonexpansive in the intermediate mapping from C into itself. In this paper, we first provide a ergodic retraction theorem and a mean ergodic convergence theorem. Using this result, we show that the set F (T ) of fixed points of T is a sunny, nonexpansive retract of C if the norm of X is u...

and Applied Analysis 3 If θ ≡ 0, the problem 1.4 reduces into the minimize problem, denoted by arg min φ , which is to find x ∈ C such that φ ( y ) − φ x ≥ 0, ∀y ∈ C. 1.7 The above formulation 1.5 was shown in 11 to covermonotone inclusion problems, saddle point problems, variational inequality problems, minimization problems, optimization problems, variational inequality problems, vector equil...

An existence theorem for a fixed point of an α-nonexpansive mapping of a nonempty bounded, closed and convex subset of a uniformly convex Banach space has been recently established by Aoyama and Kohsaka with a non-constructive argument. In this paper, we show that appropriate Ishikawa iterate algorithms ensure weak and strong convergence to a fixed point of such a mapping. Our theorems are also...

The main purpose of the present paper is to impose onesided Lipschitz condition for differential inclusions on a closed and convex domain of a uniformly convex Banach space. Both differential inclusions with almost upper demicontinuous and almost lower semicontinuous right–hand sides are considered. The existence theorems are proved and it is shown that the set of solutions is connected. AMS Ma...

Let $C$ be a nonempty closed convex subset of a real Banach space $E$, let $B: C rightarrow E $ be a nonlinear map, and let  $u, v$ be  positive numbers. In this paper, we show  that  the generalized variational inequality $V I (C, B)$ is singleton for $(u, v)$-cocoercive mappings under appropriate assumptions on Banach spaces. The main results are extensions of the Saeidi's Propositions for fi...

Let $Omega_X$ be a bounded, circular and strictly convex domain of a Banach space $X$ and $mathcal{H}(Omega_X)$ denote the space of all holomorphic functions defined on $Omega_X$. The growth space $mathcal{A}^omega(Omega_X)$ is the space of all $finmathcal{H}(Omega_X)$ for which $$|f(x)|leqslant C omega(r_{Omega_X}(x)),quad xin Omega_X,$$ for some constant $C>0$, whenever $r_{Omega_X}$ is the M...

‎We use of two notions functionally convex (briefly‎, ‎F--convex) and functionally closed (briefly‎, ‎F--closed) in functional analysis and obtain more results‎. ‎We show that if $lbrace A_{alpha} rbrace _{alpha in I}$ is a family $F$--convex subsets with non empty intersection of a Banach space $X$‎, ‎then $bigcup_{alphain I}A_{alpha}$ is F--convex‎. ‎Moreover‎, ‎we introduce new definition o...

An analytic function f(z)= z+an+1zn+1+··· , defined on the unit disk = {z : |z|< 1}, is in the class Sp if zf ′(z)/f(z) is in the parabolic region Rew > |w −1|. This class is closely related to the class of uniformly convex functions. Sufficient conditions for function to be in Sp are obtained. In particular, we find condition on λ such that the function f(z), satisfying (1−α)(f(z)/z)μ+αf ′(z)(...

Making use of the Dziok-Srivastava operator, we introduce a new class of complex valued harmonic functions which are orientation preserving and univalent in the open unit disc and are related to uniformly convex functions. We investigate the coefficient bounds, distortion inequalities and extreme points for this generalized class of functions.