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In this paper, we consider the problem of constructing new optimal explicit and implicit Adams-type difference formulas for finding an approximate solution to the Cauchy problem for an ordinary differential equation in a Hilbert space. In this work, I minimize the norm of the error functional of the difference formula with respect to the coefficients, we obtain a system of linear algebraic equations for the coefficients of the difference formulas. This system of equations is reduced to a system of equations in convolution and the system of equations is completely solved using a discrete analog of a differential operator d²/dx² - 1. Here we present an algorithm for constructing optimal explicit and implicit difference formulas in a specific Hilbert space. In addition, comparing the Euler method with optimal explicit and implicit difference formulas, numerical experiments are given. Experiments show that the optimal formulas give a good approximation compared to the Euler method. [ABSTRACT FROM AUTHOR]

With this paper, we purpose to introduce and characterized some generalized classes of completely monotone functions on some types of white noise spaces [ABSTRACT FROM AUTHOR]

The aim of this paper is to introduce a fully modified (p,q)-poly-Euler polynomials and numbers of the first type. We investigate some properties that is related with (p; q)-Gaussian binomials coefficients. We also construct (p; q)- analogue of the Stirling numbers of the second kind and fully modified (p,q)-poly-Euler polynomials and numbers of the first type with two variables. [ABSTRACT FROM AUTHOR]

In this paper, we construct higher-order q-poly-tangent numbers and polynomials and give several properties, including addition formula and multiplication formula. Finally, we explore the distribution of roots of higher-order q-poly-tangent polynomials. [ABSTRACT FROM AUTHOR]

The purpose of this paper is to study by applying the makgeolli structure to commutative ideal in BCK-algebras. The notion of commutative makgeolli ideal is introduced, and their properties are investigated. The relationship between makgeolli ideal and commutative makgeolli ideal is discussed. Example to show that a makgeolli ideal may not be a commutative makgeolli ideal is provided, and then the conditions under which a makgeolli ideal can be a commutative makgeolli ideal are explored. A new commutative makgeolli ideal is established using the given commutative makgeolli ideal, and characterizations of a commutative makgeolli ideal are displayed. Finally, the extension property for a commutative makgeolli ideal is established. [ABSTRACT FROM AUTHOR]

In this paper, we introduce a general composite iterative algorithm for findinding a common element of the set of solutions of variational inequality problem for a hemicontinuous monotone mapping and the set of fixed points of a hemicontinuous pseudocontractive mapping in a Hilbert space. Under suitable control conditions, we establish strong convergence of the sequence generated by the proposed iterative algorithm to a common element of two sets, which is the unique solution of a certain variational inequality related to a boundedly Lipschitzian and strongly monotone mapping. As a consequence, we obtain the unique minimum-norm common point of two sets. [ABSTRACT FROM AUTHOR]

Fuzzy number (FN) plays a vital role in decision making problems as it is used to represent the uncertain terms. Researchers in the field of decision-making analysis have used triangular and trapezoidal FN to solve the problem in the uncertain environment. FN have also been extended recently such as pentagonal, hexagonal, and heptagonal and so on. This paper aims to generalize the Hexadecagonal fuzzy number (GHFN) which contains set of 16-tuples. Membership functions and alpha cuts of linear and nonlinear GHFN with symmetry and asymmetry have also been derived. [ABSTRACT FROM AUTHOR]

In this paper, we introduce two iterative algorithms for finding the solution of the sum of two monotone operators by using hybrid projection methods and shrinking projection methods. Under some suitable conditions, we prove strong convergence theorems of such sequences to the solution of the sum of an inverse-strongly monotone and a maximal monotone operator. Finally, we present a numerical result of our algorithm which defined by the hybrid method. [ABSTRACT FROM AUTHOR]

In this paper, we introduce and solve the following additive-additive (s, t)-functional inequality ||g(x+y+z) - g(x) g(y) g(2)|| +||h(x+y+z) + h(x-2y+z) + h(x+y-2z) - 3h(x)||....(0.1) ≤|| s (3g (x+y+z/3)-g(x)-g(y) - g(z)|| + t (3h (x+y+z/3) + h(x-2y+z) + h(x+y-2z) -3h(x)||, wheres and t are fixed nonzero complex numbers with s < 1 and t < 1. Using the direct method and the fixed point method, we prove the Hyers-Ulam stability of ternary hom- derivations and ternary homomorphisms in C-ternary algebras, associated to the additive- additive (s, t)-functional inequality (0.1) and the following functional inequality ||g([x, y, z]) [g(x), h(y), h(z)]-[h(x), g(y), h(z)] - [h(x), h(y), g(z)]|| +||h([x, y, z]) - [h(x), h(y), h(z)]|| ≤ φ(x, y, z). [ABSTRACT FROM AUTHOR]

In this paper, we find solutions and investigate the superstability bounded by function for the sine functional equation (S) from the approximate inequality of the Pexider type functional equation: f (x+y/2)²-g(x-y/2)2 = h(x)k(y). Furthermore, the results are extended to Banach algebras. As a consequence, we obtain the superstability for the exponential functional equations, the hyperbolic functional equations, and the jointed Pexider Lobacevski equation. [ABSTRACT FROM AUTHOR]

In this paper we introduce the notion of liner fuzzy real numbers, and show that the set of all positive (or negative) symmetric linear fuzzy real numbers forms a semiring. Moreover, we discuss a complex transform of linear fuzzy real numbers. [ABSTRACT FROM AUTHOR]

In this paper we study linear abstract Cauchy problem in two variables. Theory of two-parameter semigroups of linear operators and tensor product of Banach spaces is needed to study the solution of such equation. [ABSTRACT FROM AUTHOR]

Let H(D) be the set of all analytic functions on the open unit disk D of C, u є H(D) and Φ an entire function on C. In this paper, we characterize the boundedness and compactness of the weighted differentiation superposition operator Dum SΦ from H∞ to the nth weighted-type space. [ABSTRACT FROM AUTHOR]

A Lie point symmetry analysis of a class of higher order difference equations with variable coefficients is considered and new symmetries are found. These symmetries are utilized to investigate the existence of solutions. The results in this paper generalize some results in the literature. [ABSTRACT FROM AUTHOR]