pure rotation about a fixed point

... Stability of a generalized quadratic functional equation in various spaces: a fixed point alternative approach Hassan Azadi Kenary1 , Choonkil Park∗2 , Hamid Rezaei1 and Sun Young Jang3 Department ... of Mathematics, University of Ulsan, Ulsan 680-749, Korea ∗ Corresponding author: baak@hanyang.ac.kr Email addresses: HAK: azadi@mail.yu.ac.ir HR: rezaei@mail.yu.ac.ir SYJ: jsym@ulsan.ac.kr Abstract ... | · | is called a non-Archimedean valuation, and the field is called a non-Archimedean field Clearly, |1| = | − 1| = and |n| ≤ for all n ∈ N A trivial example of a non-Archimedean valuation is the...

Ngày tải lên: 18/06/2014, 22:20

... Stability of a generalized quadratic functional equation in various spaces: a fixed point alternative approach Hassan Azadi Kenary1 , Choonkil Park∗2 , Hamid Rezaei1 and Sun Young Jang3 Department ... of Mathematics, University of Ulsan, Ulsan 680-749, Korea ∗ Corresponding author: baak@hanyang.ac.kr Email addresses: HAK: azadi@mail.yu.ac.ir HR: rezaei@mail.yu.ac.ir SYJ: jsym@ulsan.ac.kr Abstract ... | · | is called a non-Archimedean valuation, and the field is called a non-Archimedean field Clearly, |1| = | − 1| = and |n| ≤ for all n ∈ N A trivial example of a non-Archimedean valuation is the...

Ngày tải lên: 20/06/2014, 04:20

... Gnana Bhaskar, T, Lakshmikantham, V: Fixed point theorems in partially ordered metric spaces and applications Nonlinear Anal 65, 1379–1393 (2006) doi:10.1016/j.na.2005.10.017 Harjani, J, Sadarangani, ... which are fixed points of T and z ≠ y We consider two cases Case 1: Suppose that z and y are comparable Without loss of generality, we suppose z

Ngày tải lên: 20/06/2014, 22:20

... equation and a Jensen-quadratic equation Abstr Appl Anal 2007 (2007) Article ID 45179 Găvruta, P: A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings J Math Anal Appl ... doi:10.1186/1029-242X-2011-82 Cite this article as: Bae and Park: A fixed- point approach to the stability of a functional equation on quadratic forms Journal of Inequalities and Applications 2011 2011:82 Page of ... S0002-9939-1978-0507327-1 12 Park, W-G, Bae, J-H: A functional equation originating from quadratic forms J Math Anal Appl 326, 1142–1148 (2007) doi:10.1016/j.jmaa.2006.03.023 13 Margolis, B, Dias, JB: A fixed point...

Ngày tải lên: 20/06/2014, 22:20

... ∈ A , and a mapping R : A → A is a quadratic right centralizer if R is a quadratic homogeneous mapping and R(ab) = a2 R(b) for all a, b ∈ A Also a quadratic double centralizer of an algebra A ... that a mapping L : A → A is a quadratic left centralizer if L is a quadratic homogeneous mapping, that is quadratic and L(la) = l2 L (a) for all a ∈ A and l Î ℂ and L(ab) = L (a) b2 for all a, ... quadratic multipliers Assume that A is a complex Banach algebra Recall that a mapping T : A → A is a quadratic multiplier if T is a quadratic homogeneous mapping, and a2 T(b) = T (a) b2 for all a, ...

Ngày tải lên: 20/06/2014, 22:20

... Del Circolo Math Di Palermo (to appear) Kenary, HA, Shafaat, Kh, Shafei, M, Takbiri, G: Hyers-Ulam-Rassias stability of the Appollonius quadratic mapping in RNspaces J Nonlinear Sci Appl 4, 110–119 ... equation J Inequal Appl 2011 (2011) Article ID 194394 13 Kenary, HA: On the Hyers-Ulam-Rassias stability of a functional equation in non-Archimedean and random normed spaces Acta Universitatis Apulensis ... Găvruta, P: A generalization of the Hyers-Ulam-Rassias stability of approximately additive mappings J Math Anal Appl 184, 431–436 (1994) doi:10.1006/jmaa.1994.1211 Skof, F: Local properties and approximation...

Ngày tải lên: 20/06/2014, 22:20

... mapping, that is L λ2 L a , for all a ∈ A and λ ∈ C, and L ab L a b2 , for all a, b ∈ A is quadratic and L a A mapping R : A → A is a quadratic right centralizer if R is a quadratic homogeneous mapping ... mapping and R ab a2 R b , for all a, b ∈ A Also, a quadratic double centralizer of an algebra A is a pair L, R where L is a quadratic left centralizer, R is a quadratic right R a b2 , for all a, b ... Multipliers Assume that A is a complex Banach algebra Recall that a mapping T : A → A is a quadratic T a b2 , for all a, b ∈ A see multiplier if T is a quadratic homogeneous mapping, and a2 T b 16...

Ngày tải lên: 21/06/2014, 05:20

... generalized strongly nonlinear quasivariational inequalities,” Journal of Mathematical Analysis and Applications, vol 201, no 1, pp 180–194, 1996 13 L.-C Ceng, S Huang, and A Petrusel, “Weak convergence ... Verma, “Iterative algorithms and a new system of nonlinear quasivariational inequalities,” Advances in Nonlinear Variational Inequalities, vol 4, no 1, pp 117–124, 2001 29 L.-C Ceng, C Wang, and ... Yao, Y.-C Liou, and S M Kang, “Approach to common elements of variational inequality problems and fixed point problems via a relaxed extragradient method,” Computers & Mathematics with Applications,...

Ngày tải lên: 21/06/2014, 07:20

... type additive, quadratic, cubic and quartic functional equation,” in Nonlinear Analysis and Variational Problems, P M Pardalos, Th M Rassias, and A A Khan, Eds., Springer Optimization and Its Applications, ... point approach,” Abstract and Applied Analysis, vol 2009, Article ID 360432, 17 pages, 2009 27 C Park and J S An, “Stability of the Cauchy-Jensen functional equation in C∗ -algebras: a fixed point ... additive mappings,” Journal of Mathematical Analysis and Applications, vol 184, no 3, pp 431–436, 1994 P Gavruta, “An answer to a question of Th M Rassias and J Tabor on mixed stability of mappings,”...

Ngày tải lên: 21/06/2014, 18:20

... functional equations,” Aequationes Mathematicae, vol 27, no 1-2, pp 76–86, 1984 K.-W Jun and Y.-H Lee, “On the Hyers-Ulam-Rassias stability of a Pexiderized quadratic inequality,” Mathematical Inequalities ... Journal of Mathematical Analysis and Applications, vol 343, no 1, pp 567–572, 2008 23 O Hadˇ i´ , E Pap, and V Radu, “Generalized contraction mapping principles in probabilistic metric zc spaces,” ... equations 14, 20 A comparison between the direct method and fixed alternative method for functional equations is given in 19 The fixed alternative method can be considered as an advantage of this method...

Ngày tải lên: 21/06/2014, 20:20

... Rassias and K Shibata, “Variational problem of some quadratic functionals in complex analysis,” Journal of Mathematical Analysis and Applications, vol 228, no 1, pp 234–253, 1998 68 K Ravi and ... Eshaghi-Gordji, S Abbaszadeh, and C Park, “On the stability of a generalized quadratic and quartic type functional equation in quasi-Banach spaces,” preprint Fixed Point Theory and Applications 23 29 ... vruta, A generalization of the Hyers-Ulam-Rassias stability of approximately additive a ¸ mappings,” Journal of Mathematical Analysis and Applications, vol 184, no 3, pp 431–436, 1994 18 J M Rassias,...

Ngày tải lên: 21/06/2014, 20:20

... Miranda’s theorem,” Analele Universitatii din Craiova Seria Matematica Informatica, vol 27, pp 6–13, 2000 Uwe Sch¨ fer: Institut f¨ r Angewandte und Numerische Mathematik, Fakult¨ t f¨ r Mathematik, ... Matematica, vol 37, no 2, pp 161–164, 1991 [7] C Avramescu, A generalization of Miranda’s theorem,” Seminar on Fixed Point Theory ClujNapoca, vol 3, pp 121–127, 2002 [8] C Avramescu, “Some remarks about ... was started References [1] C Miranda, “Un’osservazione su un teorema di Brouwer,” Bollettino dell’Unione Matematica Italiana, vol 3, pp 5–7, 1940 [2] M N Vrahatis, A short proof and a generalization...

Ngày tải lên: 22/06/2014, 06:20

... Differential Equations and Their Applications, Birkh¨ user, Boston, Mass, USA, 1998 a S.-M Jung, Hyers-Ulam-Rassias Stability of Functional Equations in Mathematical Analysis, Hadronic Press, Palm Harbor, ... “Approximate homomorphisms,” Aequationes Mathematicae, vol 44, no 2-3, pp 125–153, 1992 11 Th M Rassias, “On the stability of functional equations and a problem of Ulam,” Acta Applicandae Mathematicae, ... point approach to the stability of an equation of the square spiral,” Banach Journal of Mathematical Analysis, vol 1, no 2, pp 148–153, 2007 14 S.-M Jung and J M Rassias, “Stability of general Newton...

Ngày tải lên: 22/06/2014, 11:20

... in Mathematical Analysis, Hadronic Press, Palm Harbor, Fla, USA, 2001 [10] Th M Rassias, “On the stability of functional equations and a problem of Ulam,” Acta Applicandae Mathematicae, vol 62, ... paper, we will adopt the idea of C˘ dariu and Radu [12] and prove the Hyersa Ulam-Rassias stability and the Hyers-Ulam stability of the Volterra integral equation (1.2) Hyers-Ulam-Rassias stability ... additive a ¸ mappings,” Journal of Mathematical Analysis and Applications, vol 184, no 3, pp 431–436, 1994 [6] D H Hyers, G Isac, and Th M Rassias, Stability of Functional Equations in Several Variables,...

Ngày tải lên: 22/06/2014, 19:20

... Miranda’s theorem,” Analele Universitatii din Craiova Seria Matematica Informatica, vol 27, pp 6–13, 2000 Uwe Sch¨ fer: Institut f¨ r Angewandte und Numerische Mathematik, Fakult¨ t f¨ r Mathematik, ... Matematica, vol 37, no 2, pp 161–164, 1991 [7] C Avramescu, A generalization of Miranda’s theorem,” Seminar on Fixed Point Theory ClujNapoca, vol 3, pp 121–127, 2002 [8] C Avramescu, “Some remarks about ... was started References [1] C Miranda, “Un’osservazione su un teorema di Brouwer,” Bollettino dell’Unione Matematica Italiana, vol 3, pp 5–7, 1940 [2] M N Vrahatis, A short proof and a generalization...

Ngày tải lên: 22/06/2014, 19:20

... [5] V Azhmyakov, Stable Operators in Analysis and Optimization, Peter Lang, Berlin, 2005 [6] C Baiocchi and A Capelo, Variational and Quasivariational Inequalities Applications to Free Boundary ... equation As a corollary of the general solvability results, we obtain a fixed point theorem for a family of Fr´ chet differentiable expanding operators in real Banach spaces e Some examples of stable ... This shows that R (A (x0 )) is also a Banach space By the Banach open mapping theorem, the operator (A (x0 ))−1 is linear and continuous Recall the definition of a linear compact operator [23] Definition...

Ngày tải lên: 22/06/2014, 22:20

... mapping and so for each a ∈ X, Ua admits a unique fixed point, it is denoted by φ (a) , then Ua φ (a) = φ (a) ⇐⇒ U φ (a) + a = φ (a) ⇐⇒ φ (a) = (I − U)−1 (a) (2.4) m Let u0 be a fixed point of U For each ... Foundations of Modern Analysis, Academic Press, New York, 1969 e [6] L H Hoa and K Schmitt, Fixed point theorems of Krasnosel’skii type in locally convex spaces and applications to integral equations, ... Nonlinear Functional Analysis and Its Applications I, Springer, New York, 1986 Le Thi Phuong Ngoc: Department of Natural Science, Nha Trang Educational College, 01 Nguyen Chanh Street, Nha Trang...

Ngày tải lên: 22/06/2014, 22:20

... and B D MacCluer, Composition Operators on Spaces of Analytic Functions, Studies in Advanced Mathematics, CRC Press, Florida, 1995 J B Garnett, Bounded Analytic Functions, Pure and Applied Mathematics, ... Julia’s lemma In case ϕ has a fixed point, but is not the identity or an elliptic disk automorphism, one can use Schwarz’s lemma in classical complex analysis to show that {ϕ[n] } tends to that ... Springer-Verlag, New York, 1993 Valentin Matache: Department of Mathematics, University of Nebraska, Omaha, NE 68182, USA E-mail address: vmatache@mail.unomaha.edu ...

Ngày tải lên: 23/06/2014, 00:20

... is a circle Author is grateful to Alexey Pakharev for help in preparation of this text References [1] A V Akopyan Rotation of isogonal point Journal of classical geometry:74, 1, 2012 Moscow State ... that locus of points P is a circle It is clear that the transformation which maps H to P is a composition of an inversion, a parallel transform and rotations Indeed, denote by zx the coordinate ... REFERENCES 67 points A , A, P , and Q are cocyclic Similarly the quadrilateral P B ∗ BQ is inscribed in a circle Let lines AA∗ and BB ∗ intersect in a point F Indeed ABQH ∼ A B ∗ P H, so ∠(BQ, QA) =...

Ngày tải lên: 18/07/2014, 22:48

... Uniformly lipschitzian families of transformations in Banach spaces, Canad J Math 26 (1974) 1245–1256 W A Kirk, A fixed point theorem for mappings which not increase distances, Amer Math Monthly 72 ... Nonexpansive Mappings in Locally Convex Spaces 151 Clearly F is a nonempty family, since C ∈ F By weakly compactnees of C and Zorn’s Lemma, F has a minimal element H Now we shall show that H consists ... Ling, Fixed points of nonexpansive maps on locally convex spaces, Bull Korean Math Soc 37 (2000) 21–36 B Schweizer and A Sklar, Probabilistic Metric Spaces, Elsevier North Holland, 1983 Do Hong Tan...

Ngày tải lên: 06/08/2014, 05:20