Objective: This study aimed to compare the effectiveness of schema therapy with acceptance and commitment therapy with exposure techniques on cognitive avoidance in female patients with generalized anxiety disorder. Methods: 10 women with generalized anxiety disorder were selected through purposeful sampling with Structured Clinical Interview for DSM Disorders (SCID-5). To determine the absenc...

and Applied Analysis 3 Definition 2.2 see 16 . Let ψ : R → R be a locally Lipschitz function, then ψ◦ u;v denotes Clarke’s generalized directional derivative of ψ at u ∈ R in the direction v and is defined as ψ◦ u;v lim sup y→u t→ 0 ψ ( y tv ) − ψ(y) t . 2.4 Clarke’s generalized gradient of ψ at u is denoted by ∂ψ u and is defined as ∂ψ u { ξ ∈ R | ψ◦ u;v ≥ 〈ξ, v〉, ∀v ∈ Rn}. 2.5 Let f : R → R b...

Abstract. In this paper, we introduce three new broad classes of secondorder generalized convex functions, namely, (F , b, φ, ρ, θ)-sounivex functions, (F , b, φ, ρ, θ)-pseudosounivex functions, and (F , b, φ, ρ, θ)-quasisounivex functions; formulate eight general second-order duality models; and prove appropriate duality theorems under various generalized (F , b, φ, ρ, θ)-sounivexity assumptio...

Given a subset X of a Dedekind domain D, and a polynomial F # D[x], the fixed divisor d(X, F ) of F over X is defined to be the ideal in D generated by the elements F(a), a # X. In this paper we derive a simple expression for d(X, F ) explicitly in terms of the coefficients of F, using a generalized notion of ``factorial'' introduced by the author in a previous paper. When X=D=Z, this generaliz...

Using the fixed point method, we prove the generalized Hyers-Ulam-Rassias stability of the following functional equation in multi-Banach spaces:begin{equation} sum_{ j = 1}^{n}fBig(-2 x_{j} + sum_{ i = 1, ineq j}^{n} x_{i}Big) =(n-6) fBig(sum_{ i = 1}^{n} x_{i}Big) + 9 sum_{ i = 1}^{n}f(x_{i}).end{equation}

Generalized Fibonacci cube Qd(f) is introduced as the graph obtained from the d-cube Qd by removing all vertices that contain a given binary string f as a substring. In this notation the Fibonacci cube Γd is Qd(11). The question whether Qd(f) is an isometric subgraph of Qd is studied. Embeddable and nonembeddable infinite series are given. The question is completely solved for strings f of leng...

We generalized the Lodha-Moore group into $n$-adic and showed analogues in of properties between Thompson $F$ $F(n)$.

We consider the problem of computing wavelet coefficients of compactly supported functions from their Fourier samples. For this, we use the recently introduced framework of generalized sampling in the context of compactly supported orthonormal wavelet bases. Our first result demonstrates that using generalized sampling one obtains a stable and accurate reconstruction, provided the number of Fou...

Let R be a commutative ring with identity. By a Bres̃ar generalized derivation of R we mean an additive map g : R→ R such that g (xy) = g (x) y + xd (y) for all x, y ∈ R, where d is a derivation of R. And an additive mapping f : R → R is called a generalized derivation in the sense of Nakajima if it satisfies f(xy) = f(x)y + xf(y) − xf(1)y for all x, y ∈ R. In this paper we extend some results o...

and Applied Analysis 3 Theorem 1.3 see 26–28 . Let X, d be a complete generalized metric space and let J : X → X be a strictly contractive mapping with Lipschitz constant L < 1. Then for each given element x ∈ X, either d ( Jx, J 1x ) ∞ 1.7 for all nonnegative integers n or there exists a positive integer n0 such that 1 d Jx, J 1x < ∞, for all n ≥ n0; 2 the sequence {Jnx} converges to a fixed p...