and Applied Analysis 3 the fixed point theory and that a Banach space X has property L if and only if it is reflexive and has the uniform Opial property. For a real vector space X, a function ρ : X → 0,∞ is called amodular if it satisfies the following conditions: i ρ x 0 if and only if x 0; ii ρ αx ρ x for all scalar α with |α| 1; iii ρ αx βy ≤ ρ x ρ y , for all x, y ∈ X and all α, β ≥ 0 with ...

A mixed-addenda W/Mo hybrid polyoxometalate cluster - K 6 [P 2 W 15 Mo O 61 (POC H 5 ) ] ( 1 was synthesized from the condensation of 10 and phenylphosphonic acid under acidic conditions. Single-crystal X-ray diffraction confirmed structure presence two centers in cap lacunary cluster. The electronic effects metal substitution were studied by cyclic voltammetry, spectroelectrochemistry electron...

We obtain lacunary recurrent relations with gaps of length four for the Bernoulli and Euler polynomials and, as a consequence, known new numbers.

The rational self-assembly of mono-lacunary Keggin clusters with 4d and 4f metal salts via a conventional method has yielded two novel polyoxometalate-based 4d-4f heterometallic compounds containing lacunary Keggin anions connected to ten metal atoms: {[Ag{Ag2(H2O)4}{Ln(H2O)6}2H ⊂ {SiW11Ln(H2O)4O39}2]·nH2O (Ln = Ce and n = 7 for 1, Ln = Pr and n = 3 for 2). Their structures were determined by s...

Based on the concept of lacunary statistical convergence sequences fuzzy numbers, convergence, uniformly and equi-lacunary double fuzzy-valued functions are defined investigated in this paper. The relationship among functions, their representations ? -level cuts discussed. In addition, we obtain form Egorov’s theorem for...