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ISSN : 1226-0657
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Vol.23 No.1
Abstract
This paper shows that the solutions to the perturbed differential system <TEX>$y^{\prime}=f(t, y)+\int_{to}^{t}g(s,y(s),Ty(s))ds+h(t,y(t))$</TEX> have asymptotic property and uniform Lipschitz stability. To show these properties, we impose conditions on the perturbed part <TEX>$\int_{to}^{t}g(s,y(s),Ty(s))ds+h(t,y(t))$</TEX>, and on the fundamental matrix of the unperturbed system y' = f(t, y).
Abstract
In this paper, we study some characterizations of unbounded domains. Among these, so-called G-domain is introduced by Cabre for the Aleksandrov-Bakelman-Pucci maximum principle of second order linear elliptic operator in a non-divergence form. This domain is generalized to wG-domain by Vitolo for the maximum principle of an unbounded domain, which contains G-domain. We study the properties of these domains and compare some other characterizations. We prove that sA-domain is wG-domain, but using the Cantor set, we are able to construct a example which is wG-domain but not sA-domain.
Abstract
In this paper, we construct a strictly increasing continuous singular function which has a simple algebraic expression.
Abstract
We establish coincidence point theorem for g-nondecreasing mappings satisfying generalized nonlinear contraction on partially ordered metric spaces. We also obtain the coupled coincidence point theorem for generalized compatible pair of mappings F, G : X<sup>2</sup> → X by using obtained coincidence point results. Furthermore, an example is also given to demonstrate the degree of validity of our hypothesis. Our results generalize, modify, improve and sharpen several well-known results.
Abstract
Let G be a finite group containing a non-abelian Sylow 2-subgroup. We elementarily show that every G-Galois field extension L/K has a hyperbolic trace form in the presence of root of unity.
Abstract
In this paper, a boundary version of the Schwarz lemma for the holom- rophic function satisfying f(a) = b, |a| < 1, b ∈ ℂ and ℜf(z) > α, 0 ≤ α < |b| for |z| < 1 is invetigated. Also, we estimate a modulus of the angular derivative of f(z) function at the boundary point c with ℜf(c) = a. The sharpness of these inequalities is also proved.
Abstract
We establish a coupled coincidence point theorem for generalized com-patible pair of mappings under generalized nonlinear contraction on a partially or-dered metric space. We also deduce certain coupled fixed point results without mixed monotone property of F : X × X → X . An example supporting to our result has also been cited. As an application the solution of integral equations are obtained here to illustrate the usability of the obtained results. We improve, extend and generalize several known results.
Abstract
We give representations of differential operators and rules for addition and multiplication of dual quaternions. Also, we research the notions and properties of a regular function and a corresponding harmonic function with values in dual quaternions of Clifford analysis.