[PDF] Top 20 A strong convergence theorem of common elements in Hilbert spaces

... Corollary . Let C be a nonempty, closed and convex subset of a real Hilbert space H. Let F be a bifunction from C × C to R which satisfies (A)-(A) and A : C → H be a κ - inverse-strongly monotone mapping. Let S ... See full document

... for all x, y ∈ C, where φx, y x 2 −2x, Jyy 2 for all x, y ∈ E; see, for instance, Kohsaka and Takahashi 10. In the case when E is a Hilbert space, we know that φx, y x − y 2 for all x, y ∈ E. Then a nonspreading ... See full document

... The theory of Variational Inequality Problems (VIP) is well known, developed and appears to be one of the most important aspect in optimization and nonlinear analysis, since most mathematical problems can be modelled as ... See full document

... Motivated and inspired by the research going on in the sections of equilibrium prob- lems and split feasibility problems, the purpose of this article is to introduce an iterative algorithm for equilibrium problems and ... See full document

... Let H be a real Hilbert space with the inner product ·, ·, which induces the norm · . Let C be a nonempty, closed, and convex subset of H. Let T be a nonlinear mapping of C into itself; we denote with Fix(T ) the ... See full document

... in Hilbert spaces. We established the strong convergence theorem and gave a numerical test to illustrate our main ...determining common solutions of fixed point problems and ... See full document

... a common element of the set of fixed point problem and the set of equilibrium problem in Hilbert spaces, for instance, [2, 3, ...the strong convergence theorem for finding ... See full document

... real Hilbert space; Marino and Xu [] proved a strong convergence theorem for strict- pseudo-contractions in a real Hilbert space; Zhou [] extended Marino and Xu’s strong ... See full document

... both Hilbert and Banach spaces were widely investigated by many au- thors (see ...a strong convergence theorem to a fixed point of a nonexpansive mapping in a Hilbert space by ... See full document

... Theorem PP Let H be a real Hilbert space, let F be a bifunction from H × H → R satisfying (A)-(A) and let T be a nonexpansive mapping on H such that F(T ) ∩ EP(F) = ∅ . Let f be a contraction of H into ... See full document

... Throughout this paper, we always assume that H is a real Hilbert space, whose inner product and norm are denoted by ·, · and · . → and are denoted by strong convergence and weak convergence, ... See full document

... Banach spaces to prove a strong convergence theorem for finding a common element of the set of fixed points of finite families of nonexpansive and strictly pseudo- contractive mappings and ... See full document

... gence theorem for the split common fixed point problem of quasi-nonexpansive map- pings in Hilbert ...split common fixed point of other nonlinear mappings, such as nonspreading type mappings ... See full document

... a common solution of the minimization problem (MP) for a convex and continuously Fréchet differentiable functional and the common fixed point problem of an infinite family of nonexpansive mappings in the ... See full document

... The conditions on the variational inequality in Theorem 2.1 have been used and generalized by several authors; see, e.g., [8], [9] and the references therein. The existence of a non-zero solution to the ... See full document

... Suzuki, “On strong convergence to common fixed points of nonexpansive semigroups in Hilbert spaces,” Proceedings of the American Mathematical Society , vol. Xu, “A strong convergence the[r] ... See full document

... , convergence . From the Riesz representation theorem , this definition of weak convergence for sequences in a Hilbert space is a special case of Definition of weak convergence in a ... See full document

... A strong convergence theorem for approximation of common fixed points of finite family of k  strictly asymptotically pseudo-contractive mappings is proved in Banach spaces using the ... See full document

... Throughout this paper, we always assume that H is a real Hilbert space with the inner product · , · and norm · . We denote by I the identity operator on H, and by Fix(T) the set of the fixed points of an operator T ... See full document

... We introduce two iterative algorithms for nonexpansive mappings in Hilbert spaces. We prove that the proposed algorithms strongly converge to a fixed point of a nonexpansive mapping T . Copyright q 2009 ... See full document