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Vol.25 No.2
Abstract
We consider the boundary value problem with a Dirichlet condition for a second order linear uniformly elliptic operator in a non-divergence form. We study some properties of a barrier at infinity which was introduced by Meyers and Serrin to investigate a solution in an exterior domains. Also, we construct a modified barrier for more general domain than an exterior domain.
Abstract
We introduce some new type of admissible mappings and prove a coupled coincidence point theorem by using newly defined concepts for generalized compatible pair of mappings satisfying <TEX>${\alpha}-{\psi}$</TEX> contraction on partially ordered metric spaces. We also prove the uniqueness of a coupled fixed point for such mappings in this setup. Furthermore, we give an example and an application to integral equations to demonstrate the applicability of the obtained results. Our results generalize some recent results in the literature.
Abstract
A mathematical knot is an embedded circle in <TEX>${\mathbb{R}}^3$</TEX>. A fundamental problem in knot theory is classifying knots up to its numbers of crossing points. Knots are often distinguished by using a knot invariant, a quantity which is the same for equivalent knots. Knot polynomials are one of well known knot invariants. In 2006, J. Przytycki showed the effects of a n - move (a local change in a knot diagram) on several knot polynomials. In this paper, the authors review about knot polynomials, especially Jones polynomial, and give an alternative proof to a part of the Przytychi's result for the case n = 3 on the Jones polynomial.
Abstract
In this paper, we introduce the notion of a clean ordered Krasner hyperring and investigate some properties of it. Now, let (R, +, <TEX>${\cdot}$</TEX>, <TEX>${\leq}$</TEX>) be a clean ordered Krasner hyperring. The following is a natural question to ask: Is there a strongly regular relation <TEX>${\sigma}$</TEX> on R for which <TEX>$R/{\sigma}$</TEX> is a clean ordered ring? Our motivation to write the present paper is reply to the above question.
Abstract
We look at Toeplitz arrays on <TEX>${\mathbb{Z}}^d$</TEX> and study a characterizing property for pure discrete spectrum in terms of the periodic structures of the Toeplitz arrays.
Abstract
Lu et al. [27] defined derivations on fuzzy Banach spaces and fuzzy Lie Banach spaces and proved the Hyers-Ulam stability of derivations on fuzzy Banach spaces and fuzzy Lie Banach spaces. It is easy to show that the definitions of derivations on fuzzy Banach spaces and fuzzy Lie Banach spaces are wrong and so the results of [27] are wrong. Moreover, there are a lot of seroius problems in the statements and the proofs of the results in Sections 2 and 3. In this paper, we correct the definitions of biderivations on fuzzy Banach algebras and fuzzy Lie Banach algebras and the statements of the results in [27], and prove the corrected theorems.
Abstract
In this paper, we prove a strong convergence result under an iterative scheme for N finite asymptotically <TEX>$k_i-strictly$</TEX> pseudo-contractive mappings and a firmly nonexpansive mappings <TEX>$S_r$</TEX>. Then, we modify this algorithm to obtain a strong convergence result by hybrid methods. Our results extend and unify the corresponding ones in [1, 2, 3, 8]. In particular, some necessary and sufficient conditions for strong convergence under Algorithm 1.1 are obtained.
Abstract
In this paper, we introduce and solve the following additive (<TEX>${\rho}_1,{\rho}_2$</TEX>)-functional inequality (0.1) <TEX>$${\parallel}f(x+y+z)-f(x)-f(y)-f(z){\parallel}{\leq}{\parallel}{\rho}_1(f(x+z)-f(x)-f(z)){\parallel}+{\parallel}{\rho}_2(f(y+z)-f(y)-f(z)){\parallel}$$</TEX>, where <TEX>${\rho}_1$</TEX> and <TEX>${\rho}_2$</TEX> are fixed nonzero complex numbers with <TEX>${\mid}{\rho}_1{\mid}+{\mid}{\rho}_2{\mid}$</TEX> < 2. Using the fixed point method and the direct method, we prove the Hyers-Ulam stability of the additive (<TEX>${\rho}_1,{\rho}_2$</TEX>)-functional inequality (0.1) in complex Banach spaces.
Abstract
In this paper, the necessary and sufficient conditions are considered for biprojectivity of Banach algebras <TEX>$E_p(I)$</TEX>. As an application, we investigate biprojectivity of convolution Banach algebras A(G) and <TEX>$L^2(G)$</TEX> on a compact group G.