July 25, 2012 Tags: BANACH spaces, BESSEL functions, CHEBYSHEV approximation, CHEBYSHEV polynomials, COMPUTER programs, ERROR analysis (Mathematics), GENERALIZED anxiety disorder
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In this paper, we obtain a unique common fixed point theorem for four self maps with asymptotic regularity condition and satisfying Ciric type weak contractive condition in cone metric spaces. Our result generalizes and improves some recent results in cone metric spaces. [ABSTRACT FROM AUTHOR]
Read MoreJuly 16, 2012 Tags: BANACH spaces, CONES (Operator theory), MAPPINGS (Mathematics), METRIC spaces, NUMBERS, Real
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In this paper, an attempt is made to using recurrence relations to establish the convergence of the Harmonic mean Newton’s method used for nonlinear equations in Banach spaces. The recurrence relations for the method are derived and then an existence-uniqueness theorem is given to establish the R-order of the method to be three and a prior error bounds. Finally, some numerical applications is presented to demonstrate our approach. [ABSTRACT FROM AUTHOR]
Read MoreJuly 13, 2012 Tags: A priori, BANACH spaces, CONVERGENCE (Mathematics), HARMONIC analysis, NEWTON-Raphson method, NONLINEAR theories, POINT mappings (Mathematics)
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Using the fixed point method, we prove the Hypers-Ul am stability of the orthogonally additive-quadratic functional equation 2f (x + y/2) + 2f (x – y/2) = 3/2f(x) – 1/2f(-x) + 1/2f(y) + 1/2f(-y) (0.1) for all x, y with x ⊥ y, in non-Archimedean Banach spaces. Here ⊥ is the orthogonality in the sense of Rätz. [ABSTRACT FROM AUTHOR]
Read MoreJuly 12, 2012 Tags: BANACH spaces, CAUCHY problem, EQUATIONS, FIXED point theory, INEQUALITIES (Mathematics), ORTHOGONALIZATION methods, Quadratic, STABILITY
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Using the fixed point method, we prove the Hyers-Ulam stability of the following generalized Jensen quadratic funtional equation f ( x + y / r + sz ) + f ( x + y / r – sz ) + f ( x – y / r + sz ) + f (x – y / r – sz ) = 4 / r² f (x) + 4 / r² f (y) + 4s² f (z) in fuzzy Banach spaces. [ABSTRACT FROM AUTHOR]
Read MoreJuly 12, 2012 Tags: BANACH spaces, EQUATIONS, FIXED point theory, FUNCTIONAL equations, FUNCTIONS of complex variables, FUZZY sets, GENERALIZATION, Quadratic
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The concept Iu convergence was introduced by Baláz and Šalát [Uniform density u and corresponding Iu -convergence, Math. Comm., 11 (2006), 1-7]. Recently, Mursaleen and Edely [On the invariant mean and statistical convergence, Appl. Math. Letters, 22 (2009) 1700-1704] used the concept of invariant mean and density to study some new type of convergence methods. In this paper we generalize these two methods by using the concept of ideal convergence and invariant mean. Further we apply our method to prove a Korovkin type approximation theorem along with an example in support of our result. [ABSTRACT FROM AUTHOR]
Read MoreJuly 11, 2012 Tags: APPROXIMATION theory, BANACH spaces, CAUCHY problem, CONVERGENCE (Mathematics), GENERALIZATION, INVARIANTS, SUMMABILITY theory
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In this manuscript, Meir-Keeler contractions on partial metric spaces are introduced. It is show that if a self-mapping T on a complete partial metric spaces is a Meir-Keeler contraction, then T has a unique fixed point. [ABSTRACT FROM AUTHOR]
Read MoreJuly 9, 2012 Tags: BANACH spaces, FIXED point theory, GENERALIZATION, MAPPINGS (Mathematics), METRIC spaces, SEQUENCES (Mathematics), TOPOLOGY
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Abstract: We exhibit examples of Fréchet Montel spaces E which have a non-reflexive Fréchet quotient but such that every Banach quotient is finite-dimensional. The construction uses a method developed by Albanese and Moscatelli and requires new ingredients. Some of the main steps in the proof are presented in Section 2. They are of independent interest and show for example that the canonical inclusion between James spaces , , is strictly cosingular. This result requires a careful analysis of the block basic sequences of the canonical basis of the dual of the James space , and permits us to show that the Fréchet space has no infinite-dimensional Banach quotients. Plichko and Maslyuchenko had proved that it has no infinite-dimensional Banach subspaces. [Copyright &y& Elsevier]
Read MoreMarch 1, 2012 Tags: ALGEBRAIC spaces, BANACH spaces, DIFFERENTIAL inclusions, DIMENSIONAL analysis, MATHEMATICAL analysis, QUOTIENT rings, SINGULARITIES (Mathematics)
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Abstract: This paper focuses on the linear perturbation of dynamical systems in Banach spaces, which corresponds to a nonautonomous dynamical system admitting a nonuniform -dichotomy. We establish the robustness or roughness of nonuniform -dichotomies, in the sense that the linear dynamical system persists under a sufficiently small linear perturbation. [Copyright &y& Elsevier]
Read MoreMarch 1, 2012 Tags: BANACH spaces, DIFFERENTIABLE dynamical systems, LINEAR systems, MATHEMATICAL analysis, PERTURBATION (Mathematics), ROBUST control
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Abstract: Given a decreasing family of continuous weights on a Banach space X, we consider the weighted inductive limits of spaces of entire functions and . Motivated by recent research by D. Carando and P. Sevilla-Peris on weighted Fréchet algebras of entire functions on Banach spaces, we determine conditions on the family of weights to ensure that the corresponding weighted space is an algebra or has polynomial Schauder decompositions. We study Hörmander algebras of entire functions defined on a Banach space and we give a description of them in terms of sequence spaces. We also focus on algebra homomorphisms between these spaces and obtain a Banach–Stone type theorem for a particular decreasing family of weights. Finally, we study the spectra of these weighted algebras, endowing them with an analytic structure. [Copyright &y& Elsevier]
Read MoreMarch 1, 2012 Tags: ALGEBRAIC topology, BANACH spaces, Continuous, DECOMPOSITION (Mathematics), Entire, FUNCTIONS, HOMOMORPHISMS (Mathematics), POLYNOMIALS, SPECTRAL theory (Mathematics)
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