Matrix Transformations Between Some Vector-Valued Sequence Spaces

In this paper, we give necessary and sufficient conditions for infinite matrices mapping from the Nakano vector-valued sequence space (X, p) into any BK-space, and by using this result, we obtain the matrix characterizations from (X, p) into the sequence spaces (Y), c₀(Y, q), c(Y), _s(Y), E_r(Y), and F_r(Y), where p = (p_k) and q = (q_k) are bounded sequences of positive real numbers such that p_k 1 for all k N, r 0, and s 1.AMS Subject Classification (2000): 46A45     

An implicit iteration process for solving a fixed point problem of a finite family of multi-valued mappings in Banach spaces

This work is concerned with the strong convergence of an approximating common fixed point sequence of a finite family of multi-valued mappings in a uniformly convex and smooth Banach space using an implicit iteration scheme introduced by Xu and Ori [H.K. Xu, R.G. Ori, An implicit iteration process for nonexpansive mappings, Numer. Funct. Anal. Optim. 22 (2001) 767–773].     

The criteria of strict monotonicity and rotundity points in generalized Calderón–Lozanovskiǐ spaces

In this paper, some basic properties of the general modular space are proven. Criteria for strictly monotone points, extreme points and SU$SU$-points in generalized Calderón–Lozanovskiǐ spaces are obtained. Consequently, the sufficient and necessary conditions for the rotundity properties of such spaces are given.     

Split Null Point Problems and Fixed Point Problems for Demicontractive Multivalued Mappings

In this paper, we consider the split null point problem and the fixed point problem for multivalued mappings in Hilbert spaces. We introduce a Halpern-type algorithm for solving the problem for maximal monotone operators and demicontractive multivalued mappings, and establish a strong convergence result under some suitable conditions. Also, we apply our problem of main result to other split problems, that is, the split feasibility problem, the split equilibrium problem, and the split minimization problem. Finally, a numerical result for supporting our main result is also supplied.     

Matrix Transformations of the Maddox Vector-Valued Sequence Spaces

In this paper, we give the matrix characterizations from any normal vector-valued FK-space containing ø(X) into scalar-valued sequence space c(q) and by applying this result, we also obtain necessary and sufficient conditions for infinite matrices mapping the sequence spaces , and F_r(X,p) into the space c(q), where p = (p_k) and q = (q_k) are bounded sequences of positive real numbers and r ≥ 0.AMS Subject Classification (2000): 46A45.     

Spectrophotometric enzymatic cycling method using -glutamate dehydrogenase and -phenylglycine aminotransferase for determination of -glutamate in foods

This report describes a new spectrophotometric method capable of determining low levels of -glutamate. The assay is based on substrate cycling between -glutamate dehydrogenase (GlDH) and the novel enzyme -phenylglycine aminotransferase ( -PhgAT). In this system, GlDH converts -glutamate to 2-oxoglutarate with concomitant reduction of NAD⁺ to NADH. The 2-oxoglutarate is recycled to -glutamate in a transamination reaction catalyzed by -PhgAT using -4-hydroxyphenylglycine as an amino donor, which is converted to 4-hydroxybenzoylformate. Both NADH and 4-hydroxybenzoylformate strongly absorb UV light at 340 nm (_340nm=6.22×10³ and 8.90×10³ l mol⁻¹ cm⁻¹, respectively). The signal amplification effect of the cycling reactions is thus further enhanced by the combined absorption of the two accumulating reaction products. The standard calibration curve for -glutamate was linear from 0.2 to 20 μM, with a detection limit of 0.14 μM. Food samples can be significantly diluted before subjected to the assay, thus reducing the effects of interfering substances. Because of the unique substrate specificity of -PhgAT, -glutamate could be selectively determined in the presence of other common amino acids at relatively high concentrations. The assay was satisfactorily applied to measure -glutamate in various kinds of food products. The procedure is simple, rapid, accurate, and should be easily automated.     

An inertial forward–backward splitting method for solving inclusion problems in Hilbert spaces

In this work, our interest is in investigating the monotone inclusion problems in the framework of real Hilbert spaces. For solving this problem, we propose an inertial forward–backward splitting algorithm involving an extrapolation factor. We then prove its strong convergence under some mild conditions. Finally, we provide some applications including the numerical experiments for supporting our main theorem.     

Convergence theorem for equilibrium problem and Bregman strongly nonexpansive mappings in Banach spaces

In this paper, we present an iterative scheme for Bregman strongly nonexpansive mappings in the framework of Banach spaces. Furthermore, we prove the strong convergence theorem for finding common fixed points with the set of solutions of an equilibrium problem.