Symmetric Properties for the (h, q)-tangent Polynomials
|
|
- Arron Lane
- 6 years ago
- Views:
Transcription
1 Adv. Studies Theor. Phys., Vol. 8, 04, no. 6, HIKARI Ltd, Symmetric Properties for the h, q-tangent Polynomials C. S. Ryoo Department of Mathematics Hannam University, Daeeon , Korea Copyright c 04 C. S. Ryoo. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Abstract In [4], we studied the h, q-tangent numbers and polynomials. By using these numbers and polynomials, we give some interesting symmetric properties for the h, q-tangent polynomials. Mathematics Subect Classification: B68, S40, S80 Keywords: tangent numbers and polynomials, h, q-tangent polynomials, alternating sums, symmetric properties Introduction Throughout this paper, we always make use of the following notations: N denotes the set of natural numbers and Z + = N {0}, C denotes the set of complex numbers, denotes the ring of p-adic rational integers, Q p denotes the field of p-adic rational numbers, and C p denotes the completion of algebraic closure of Q p. Let ν p be the normalized exponential valuation of C p with p p = p νpp = p. When one talks of q-extension, q is considered in many ways such as an indeterminate, a complex number q C, or p-adic number q C p. If q C one normally assume that q <. If q C p, we normally assume that q p <p p so that q x = expx log q for x p. For g UD ={g g : C p is uniformly differentiable function},
2 60 C. S. Ryoo the fermionic p-adic invariant integral on is defined by Kim as follows: I g = gxdμ x = lim N p N x=0 If we take g x =gx + in., then we see that gx x, see[].. I g +I g =g0, see [].. In [4], we introduced the h, q-tangent numbers T h n,q and polynomials T h n,q x and investigate their properties. Let us define the h, q-tangent numbers T h n,q and polynomials T h n,q x as follows: I q hy e yt = q hy e yt dμ y = I q hy e y+xt = q hy e y+xt dμ y = T n,q h t n n!,.3 T h n,q xtn n!..4 The following elementary properties of the h, q- tangent numbers E n,q h and polynomials T n,q h x are readily derived form.,.,.3 and.4 see, for details, [4]. We, therefore, choose to omit details involved. Theorem. For h Z, we have q hx x n dμ x =T n,q h, q hy y + x n dμ y =T n,q h x. Theorem. For any positive integer n, we have T h n,q x = n k=0 n T h k,q k xn k. The alternating sums of powers of consecutive h, q-even integers In this section, we assume that q C, with q < and h Z. By using.4, we give the alternating sums of powers of consecutive h, q-even integers as follows: T n,q h t n n! = q h e t + = n q nh e nt.
3 Symmetric properties for the h, q-tangent polynomials 6 From the above, we obtain n q nh e n+kt + k n k q n kh e nt = n k q n kh e nt. By using.3and.4, we obtain T h,q kt! + k q kh By comparing coefficients of t! T h t,q! = k k q kh in the above equation, we obtain k n q nh n = k+ q kh T h h,q k+t,q. By using the above equation we arrive at the following theorem: n q nh n Theorem. Let k be a positive integer and q C with q <. Then we obtain k T h,q k = n q nh n = k+ q kh T h h,q k+t,q.. Remark. For the alternating sums of powers of consecutive even integers, we have lim T h q k,q k = n n = k+ T k+t where T x and T denote the tangent polynomials and the tangent numbers, respectively. 3 Symmetric properties for the h, q-tangent polynomials In this section, we assume that q C p and T p. In [3], Kim investigated interesting properties of symmetry p-adic invariant integral on for Bernoulli polynomials. By using same method of [3], expect for obvious modifications, we investigate interesting properties of symmetry p-adic invariant integral on for h, q-tangent polynomials. By using., we have n I g n + n I g = n k gk, k=0, t!.
4 6 C. S. Ryoo where n N,g n x =gx + n. If n is odd from the above, we obtain n gx + ndμ x+ gxdμ x = n k gk. 3. k=0 Substituting gx =q hx e xt into the above, we obtain n q hx+n e x+nt dμ x+ q hx e xt dμ x = q h e t. 3. After some elementary calculations, we have q hx+n e x+nt dμ x+ q hx e xt dμ x = + qhn e nt. q h e t + By substituting Taylor series of e xt into 3. and the above, we arrive at the following theorem: Theorem 3. Let n be odd positive integer. Then we obtain q hx e xt dμ x q hnx e ntx dμ x = T h n t m. 3.3 Let w and w be odd positive integers. By using 3.3, we have q hw x +w x e w x +w x +w w xt dμ x dμ x q hw w x e w w xt dμ x = ew w xt q hw w e w w t + q hw e w t + q hw e w t By using 3.3 and 3.4, after elementary calculations, we obtain q hw x e w x +w w xt Z dμ x p q hw x e x w t dμ x q hw w x e w w tx dμ x = T h w w xw m t m T h w w w m t m. 3.5 By using Cauchy product in the above, we have m m T h,q w w xw T h m,q w w w m t m 3.6
5 Symmetric properties for the h, q-tangent polynomials 63 By using the symmetry in 3.5, we have q hw x e w x +w w xt Z dμ x p q hw x e x w t dμ x q hw w x e w w tx dμ x = T h w w xw m t m T h w w w m t m. Thus we obtain m m T h,q w w xw T h m,q w w w m t m 3.7 By comparing coefficients tm in the both sides of 3.6 and 3.7, we arrive at the following theorem: Theorem 3. Let w and w be odd positive integers. Then we have m m T h,q w w xt h m,q w w w m w m m = T h,q w w xt h m,q w w ww m, where T h h k,q x and T k denote the h, q-tangent polynomials and the alternating sums of powers of consecutive h, q-even integers, respectively. By using Theorem., we have the following corollary: Corollary 3.3 Let w and w be odd positive integers. Then we obtain m m w m k w k x k T h k,q w T h m,q w w k=0 = m k=0 m k w wm k x k T h k,q w T h m,q w w. By using 3.5, we have w ew w xt q hw x e x w t dμ x q wh e w t 0 x +w x+w A w t = q w h q hw x e w dμ x w = q wh T h n,q w w x + w w n t n w n!. 3.8
6 64 C. S. Ryoo By using the symmetry property in 3.8, we also have w ew w xt q hw x e x w t dμ x q wh e w t 0 x +w x+w A w t = q w h q hw x e w dμ x w = q wh T h n,q w w x + w w n t n w n!. 3.9 By comparing coefficients tn n! following theorem. in the both sides of 3.8 and 3.9, we have the Theorem 3.4 Let w and w be odd positive integers. Then we obtain w w = q w h T h n,q w q w h T h n,q w w x + w w n w w x + w w n. w 3.0 Observe that if q, then 3.0 reduces to Theorem 3.4 in [5]. Substituting w = into 3.0, we arrive at the following corollary. Corollary 3.5 Let w be odd positive integer. Then we obtain References w T n,q h x =wn q h T h n,q w x + [] L. Comtet, Advances combinatorics, Riedel, Dordrecht, 974. [] T. Kim, q-volkenborn integration, Russ. J. Math. Phys. 900, [3] T. Kim, On the Symmetries of the q-bernoulli Polynomials, Abstract and Applied Analysis, , Article ID 94367, 6 pages. [4] C. S. Ryoo, On the h, q-tangent Numbers and Polynomials, Adv. Studies Theor. Phys. 7903, w.
7 Symmetric properties for the h, q-tangent polynomials 65 [5] C. S. Ryoo, A Note on the Symmetric Properties for the Tangent Polynomials, Int. Journal of Math. Analysis, 7503, [6] H. Shin, J. Zeng, The q-tangent and q-secant numbers via continued fractions, European J. Combin. 300, Received: January 9, 04
A Note on the Carlitz s Type Twisted q-tangent. Numbers and Polynomials
Applied Mathematical Sciences, Vol. 12, 2018, no. 15, 731-738 HIKARI Ltd www.m-hikari.com https://doi.org/10.12988/ams.2018.8585 A Note on the Carlitz s Type Twisted q-tangent Numbers and Polynomials Cheon
More informationSymmetric Identities for the Generalized Higher-order q-bernoulli Polynomials
Adv. Studies Theor. Phys., Vol. 8, 204, no. 6, 285-292 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/0.2988/astp.204.428 Symmetric Identities for the Generalized Higher-order -Bernoulli Polynomials Dae
More informationSymmetric properties for the degenerate q-tangent polynomials associated with p-adic integral on Z p
Global Journal of Pure and Applied Matheatics. ISSN 0973-768 Volue, Nuber 4 06, pp. 89 87 Research India Publications http://www.ripublication.co/gpa.ht Syetric properties for the degenerate q-tangent
More informationResearch Article Some Identities of the Frobenius-Euler Polynomials
Hindawi Publishing Corporation Abstract and Applied Analysis Volume 009, Article ID 639439, 7 pages doi:0.55/009/639439 Research Article Some Identities of the Frobenius-Euler Polynomials Taekyun Kim and
More informationAdvanced Studies in Theoretical Physics Vol. 8, 2014, no. 22, HIKARI Ltd,
Advanced Studies in Theoretical Physics Vol. 8, 204, no. 22, 977-982 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/0.2988/astp.204.499 Some Identities of Symmetry for the Higher-order Carlitz Bernoulli
More informationIdentities of Symmetry for Generalized Higher-Order q-euler Polynomials under S 3
Applied Mathematical Sciences, Vol. 8, 204, no. 3, 559-5597 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/0.2988/ams.204.4755 Identities of Symmetry for Generalized Higher-Order q-euler Polynomials under
More informationSymmetric Properties for Carlitz s Type (h, q)-twisted Tangent Polynomials Using Twisted (h, q)-tangent Zeta Function
International Journal of Algebra, Vol 11, 2017, no 6, 255-263 HIKARI Ltd, wwwm-hiaricom https://doiorg/1012988/ija20177728 Symmetric Properties for Carlitz s Type h, -Twisted Tangent Polynomials Using
More informationSymmetric Identities of Generalized (h, q)-euler Polynomials under Third Dihedral Group
Applied Mathematical Sciences, vol. 8, 2014, no. 145, 7207-7212 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2014.49701 Symmetric Identities of Generalized (h, )-Euler Polynomials under
More informationResearch Article On the Modified q-bernoulli Numbers of Higher Order with Weight
Abstract and Applied Analysis Volume 202, Article ID 948050, 6 pages doi:0.55/202/948050 Research Article On the Modified -Bernoulli Numbers of Higher Order with Weight T. Kim, J. Choi, 2 Y.-H. Kim, 2
More informationOn Symmetric Property for q-genocchi Polynomials and Zeta Function
Int Journal of Math Analysis, Vol 8, 2014, no 1, 9-16 HIKARI Ltd, wwwm-hiaricom http://dxdoiorg/1012988/ijma2014311275 On Symmetric Property for -Genocchi Polynomials and Zeta Function J Y Kang Department
More informationResearch Article Multivariate p-adic Fermionic q-integral on Z p and Related Multiple Zeta-Type Functions
Hindawi Publishing Corporation Abstract and Applied Analysis Volume 2008, Article ID 304539, 13 pages doi:10.1155/2008/304539 Research Article Multivariate p-adic Fermionic -Integral on Z p and Related
More informationA NOTE ON p-adic INVARIANT INTEGRAL IN THE RINGS OF p-adic INTEGERS arxiv:math/ v1 [math.nt] 5 Jun Taekyun Kim
A NOTE ON p-adic INVARIANT INTEGRAL IN THE RINGS OF p-adic INTEGERS ariv:math/0606097v1 [math.nt] 5 Jun 2006 Taekyun Kim Jangjeon Research Institute for Mathematical Sciences and Physics, 252-5 Hapcheon-Dong
More informationNew families of special numbers and polynomials arising from applications of p-adic q-integrals
Kim et al. Advances in Difference Equations (2017 2017:207 DOI 10.1186/s13662-017-1273-4 R E S E A R C H Open Access New families of special numbers and polynomials arising from applications of p-adic
More informationA Note on Carlitz s Twisted (h,q)-euler Polynomials under Symmetric Group of Degree Five
Gen. Math. Note, Vol. 33, No. 1, March 2016, pp.9-16 ISSN 2219-7184; Copyright c ICSRS Publication, 2016 www.i-cr.org Available free online at http://www.geman.in A Note on Carlitz Twited (h,)-euler Polynomial
More informationDiophantine Equations. Elementary Methods
International Mathematical Forum, Vol. 12, 2017, no. 9, 429-438 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/imf.2017.7223 Diophantine Equations. Elementary Methods Rafael Jakimczuk División Matemática,
More informationA note on the Lebesgue Radon Nikodym theorem with respect to weighted and twisted p-adic invariant integral on Z p
Notes on Number Theory and Discrete Mathematics ISSN 1310 5132 Vol. 21, 2015, No. 1, 10 17 A note on the Lebesgue Radon Nikodym theorem with resect to weighted and twisted -adic invariant integral on Z
More informationRemarks on Fuglede-Putnam Theorem for Normal Operators Modulo the Hilbert-Schmidt Class
International Mathematical Forum, Vol. 9, 2014, no. 29, 1389-1396 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/imf.2014.47141 Remarks on Fuglede-Putnam Theorem for Normal Operators Modulo the
More informationBasins of Attraction for Optimal Third Order Methods for Multiple Roots
Applied Mathematical Sciences, Vol., 6, no., 58-59 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/.988/ams.6.65 Basins of Attraction for Optimal Third Order Methods for Multiple Roots Young Hee Geum Department
More informationImprovements in Newton-Rapshon Method for Nonlinear Equations Using Modified Adomian Decomposition Method
International Journal of Mathematical Analysis Vol. 9, 2015, no. 39, 1919-1928 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2015.54124 Improvements in Newton-Rapshon Method for Nonlinear
More informationHyers-Ulam-Rassias Stability of a Quadratic-Additive Type Functional Equation on a Restricted Domain
Int. Journal of Math. Analysis, Vol. 7, 013, no. 55, 745-75 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.1988/ijma.013.394 Hyers-Ulam-Rassias Stability of a Quadratic-Additive Type Functional Equation
More informationSome Properties Related to the Generalized q-genocchi Numbers and Polynomials with Weak Weight α
Appied Mathematica Sciences, Vo. 6, 2012, no. 118, 5851-5859 Some Properties Reated to the Generaized q-genocchi Numbers and Poynomias with Weak Weight α J. Y. Kang Department of Mathematics Hannam University,
More informationThe Representation of Energy Equation by Laplace Transform
Int. Journal of Math. Analysis, Vol. 8, 24, no. 22, 93-97 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/.2988/ijma.24.442 The Representation of Energy Equation by Laplace Transform Taehee Lee and Hwajoon
More informationResearch Article A Note on the Modified q-bernoulli Numbers and Polynomials with Weight α
Abstract and Alied Analysis Volume 20, Article ID 54534, 8 ages doi:0.55/20/54534 Research Article A Note on the Modified -Bernoulli Numbers and Polynomials with Weight α T. Kim, D. V. Dolgy, 2 S. H. Lee,
More informationSolving Homogeneous Systems with Sub-matrices
Pure Mathematical Sciences, Vol 7, 218, no 1, 11-18 HIKARI Ltd, wwwm-hikaricom https://doiorg/112988/pms218843 Solving Homogeneous Systems with Sub-matrices Massoud Malek Mathematics, California State
More informationMappings of the Direct Product of B-algebras
International Journal of Algebra, Vol. 10, 2016, no. 3, 133-140 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ija.2016.615 Mappings of the Direct Product of B-algebras Jacel Angeline V. Lingcong
More informationA Generalization of p-rings
International Journal of Algebra, Vol. 9, 2015, no. 8, 395-401 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ija.2015.5848 A Generalization of p-rings Adil Yaqub Department of Mathematics University
More informationOn Symmetric Bi-Multipliers of Lattice Implication Algebras
International Mathematical Forum, Vol. 13, 2018, no. 7, 343-350 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/imf.2018.8423 On Symmetric Bi-Multipliers of Lattice Implication Algebras Kyung Ho
More informationThe Shifted Data Problems by Using Transform of Derivatives
Applied Mathematical Sciences, Vol. 8, 2014, no. 151, 7529-7534 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2014.49784 The Shifted Data Problems by Using Transform of Derivatives Hwajoon
More informationDynamical Behavior for Optimal Cubic-Order Multiple Solver
Applied Mathematical Sciences, Vol., 7, no., 5 - HIKARI Ltd, www.m-hikari.com https://doi.org/.988/ams.7.6946 Dynamical Behavior for Optimal Cubic-Order Multiple Solver Young Hee Geum Department of Applied
More informationA Family of Optimal Multipoint Root-Finding Methods Based on the Interpolating Polynomials
Applied Mathematical Sciences, Vol. 8, 2014, no. 35, 1723-1730 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2014.4127 A Family of Optimal Multipoint Root-Finding Methods Based on the Interpolating
More informationStability of a Functional Equation Related to Quadratic Mappings
International Journal of Mathematical Analysis Vol. 11, 017, no., 55-68 HIKARI Ltd, www.m-hikari.com https://doi.org/10.1988/ijma.017.610116 Stability of a Functional Equation Related to Quadratic Mappings
More informationA Remark on Certain Filtrations on the Inner Automorphism Groups of Central Division Algebras over Local Number Fields
International Journal of lgebra, Vol. 10, 2016, no. 2, 71-79 HIKRI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ija.2016.612 Remark on Certain Filtrations on the Inner utomorphism Groups of Central
More informationOn Two New Classes of Fibonacci and Lucas Reciprocal Sums with Subscripts in Arithmetic Progression
Applied Mathematical Sciences Vol. 207 no. 25 2-29 HIKARI Ltd www.m-hikari.com https://doi.org/0.2988/ams.207.7392 On Two New Classes of Fibonacci Lucas Reciprocal Sums with Subscripts in Arithmetic Progression
More informationSecond Hankel Determinant Problem for a Certain Subclass of Univalent Functions
International Journal of Mathematical Analysis Vol. 9, 05, no. 0, 493-498 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/0.988/ijma.05.55 Second Hankel Determinant Problem for a Certain Subclass of Univalent
More informationSome Properties of a Semi Dynamical System. Generated by von Forester-Losata Type. Partial Equations
Int. Journal of Math. Analysis, Vol. 7, 2013, no. 38, 1863-1868 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2013.3481 Some Properties of a Semi Dynamical System Generated by von Forester-Losata
More informationAn Abundancy Result for the Two Prime Power Case and Results for an Equations of Goormaghtigh
International Mathematical Forum, Vol. 8, 2013, no. 9, 427-432 HIKARI Ltd, www.m-hikari.com An Abundancy Result for the Two Prime Power Case and Results for an Equations of Goormaghtigh Richard F. Ryan
More informationA Fixed Point Approach to the Stability of a Quadratic-Additive Type Functional Equation in Non-Archimedean Normed Spaces
International Journal of Mathematical Analysis Vol. 9, 015, no. 30, 1477-1487 HIKARI Ltd, www.m-hikari.com http://d.doi.org/10.1988/ijma.015.53100 A Fied Point Approach to the Stability of a Quadratic-Additive
More informationOn a Principal Ideal Domain that is not a Euclidean Domain
International Mathematical Forum, Vol. 8, 013, no. 9, 1405-141 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.1988/imf.013.37144 On a Principal Ideal Domain that is not a Euclidean Domain Conan Wong
More informationSecure Weakly Connected Domination in the Join of Graphs
International Journal of Mathematical Analysis Vol. 9, 2015, no. 14, 697-702 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2015.519 Secure Weakly Connected Domination in the Join of Graphs
More informationA Generalization of Generalized Triangular Fuzzy Sets
International Journal of Mathematical Analysis Vol, 207, no 9, 433-443 HIKARI Ltd, wwwm-hikaricom https://doiorg/02988/ijma2077350 A Generalization of Generalized Triangular Fuzzy Sets Chang Il Kim Department
More informationGeneralization of the Banach Fixed Point Theorem for Mappings in (R, ϕ)-spaces
International Mathematical Forum, Vol. 10, 2015, no. 12, 579-585 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/imf.2015.5861 Generalization of the Banach Fixed Point Theorem for Mappings in (R,
More informationA Short Note on Universality of Some Quadratic Forms
International Mathematical Forum, Vol. 8, 2013, no. 12, 591-595 HIKARI Ltd, www.m-hikari.com A Short Note on Universality of Some Quadratic Forms Cherng-tiao Perng Department of Mathematics Norfolk State
More informationOn Some Identities and Generating Functions
Int. Journal of Math. Analysis, Vol. 7, 2013, no. 38, 1877-1884 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2013.35131 On Some Identities and Generating Functions for k- Pell Numbers Paula
More informationOn a Diophantine Equation 1
International Journal of Contemporary Mathematical Sciences Vol. 12, 2017, no. 2, 73-81 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ijcms.2017.728 On a Diophantine Equation 1 Xin Zhang Department
More informationResearch Article Parametric Evaluations of the Rogers-Ramanujan Continued Fraction
International Mathematics and Mathematical Sciences Volume 011, Article ID 940839, 11 pages doi:10.1155/011/940839 Research Article Parametric Evaluations of the Rogers-Ramanujan Continued Fraction Nikos
More informationGeneralized Derivation on TM Algebras
International Journal of Algebra, Vol. 7, 2013, no. 6, 251-258 HIKARI Ltd, www.m-hikari.com Generalized Derivation on TM Algebras T. Ganeshkumar Department of Mathematics M.S.S. Wakf Board College Madurai-625020,
More informationSome identities involving Changhee polynomials arising from a differential equation 1
Global Journal of Pure and Applied Mathematics. ISS 973-768 Volume, umber 6 (6), pp. 4857 4866 Research India Publications http://www.ripublication.com/gjpam.htm Some identities involving Changhee polynomials
More informationRestrained Weakly Connected Independent Domination in the Corona and Composition of Graphs
Applied Mathematical Sciences, Vol. 9, 2015, no. 20, 973-978 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2015.4121046 Restrained Weakly Connected Independent Domination in the Corona and
More informationAlternate Locations of Equilibrium Points and Poles in Complex Rational Differential Equations
International Mathematical Forum, Vol. 9, 2014, no. 35, 1725-1739 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/imf.2014.410170 Alternate Locations of Equilibrium Points and Poles in Complex
More informationAn Improved Hybrid Algorithm to Bisection Method and Newton-Raphson Method
Applied Mathematical Sciences, Vol. 11, 2017, no. 56, 2789-2797 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ams.2017.710302 An Improved Hybrid Algorithm to Bisection Method and Newton-Raphson
More informationFinite Codimensional Invariant Subspace and Uniform Algebra
Int. Journal of Math. Analysis, Vol. 8, 2014, no. 20, 967-971 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2014.4388 Finite Codimensional Invariant Subspace and Uniform Algebra Tomoko Osawa
More informationSerkan Araci, Mehmet Acikgoz, and Aynur Gürsul
Commun. Korean Math. Soc. 28 2013), No. 3, pp. 457 462 http://dx.doi.org/10.4134/ckms.2013.28.3.457 ANALYTIC CONTINUATION OF WEIGHTED q-genocchi NUMBERS AND POLYNOMIALS Serkan Araci, Mehmet Acikgoz, and
More informationStrong Convergence of the Mann Iteration for Demicontractive Mappings
Applied Mathematical Sciences, Vol. 9, 015, no. 4, 061-068 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.1988/ams.015.5166 Strong Convergence of the Mann Iteration for Demicontractive Mappings Ştefan
More informationGeneralized Boolean and Boolean-Like Rings
International Journal of Algebra, Vol. 7, 2013, no. 9, 429-438 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ija.2013.2894 Generalized Boolean and Boolean-Like Rings Hazar Abu Khuzam Department
More informationZ. Omar. Department of Mathematics School of Quantitative Sciences College of Art and Sciences Univeristi Utara Malaysia, Malaysia. Ra ft.
International Journal of Mathematical Analysis Vol. 9, 015, no. 46, 57-7 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.1988/ijma.015.57181 Developing a Single Step Hybrid Block Method with Generalized
More informationOn Positive Stable Realization for Continuous Linear Singular Systems
Int. Journal of Math. Analysis, Vol. 8, 2014, no. 8, 395-400 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2014.4246 On Positive Stable Realization for Continuous Linear Singular Systems
More informationKey Words: Genocchi numbers and polynomals, q-genocchi numbers and polynomials, q-genocchi numbers and polynomials with weight α.
Bol. Soc. Paran. Mat. 3s. v. 3 203: 7 27. c SPM ISSN-275-88 on line ISSN-0037872 in ress SPM: www.sm.uem.br/bsm doi:0.5269/bsm.v3i.484 A Note On The Generalized q-genocchi measures with weight α Hassan
More informationk-jacobsthal and k-jacobsthal Lucas Matrix Sequences
International Mathematical Forum, Vol 11, 016, no 3, 145-154 HIKARI Ltd, wwwm-hikaricom http://dxdoiorg/101988/imf0165119 k-jacobsthal and k-jacobsthal Lucas Matrix Sequences S Uygun 1 and H Eldogan Department
More informationToric Deformation of the Hankel Variety
Applied Mathematical Sciences, Vol. 10, 2016, no. 59, 2921-2925 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2016.6248 Toric Deformation of the Hankel Variety Adelina Fabiano DIATIC - Department
More informationOn Uniform Limit Theorem and Completion of Probabilistic Metric Space
Int. Journal of Math. Analysis, Vol. 8, 2014, no. 10, 455-461 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2014.4120 On Uniform Limit Theorem and Completion of Probabilistic Metric Space
More informationOn Linear Recursive Sequences with Coefficients in Arithmetic-Geometric Progressions
Applied Mathematical Sciences, Vol. 9, 015, no. 5, 595-607 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.1988/ams.015.5163 On Linear Recursive Sequences with Coefficients in Arithmetic-Geometric Progressions
More informationk-pell, k-pell-lucas and Modified k-pell Numbers: Some Identities and Norms of Hankel Matrices
International Journal of Mathematical Analysis Vol. 9, 05, no., 3-37 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/0.988/ijma.05.4370 k-pell, k-pell-lucas and Modified k-pell Numbers: Some Identities
More informationPeriodic and Soliton Solutions for a Generalized Two-Mode KdV-Burger s Type Equation
Contemporary Engineering Sciences Vol. 11 2018 no. 16 785-791 HIKARI Ltd www.m-hikari.com https://doi.org/10.12988/ces.2018.8267 Periodic and Soliton Solutions for a Generalized Two-Mode KdV-Burger s Type
More informationOn a Certain Representation in the Pairs of Normed Spaces
Applied Mathematical Sciences, Vol. 12, 2018, no. 3, 115-119 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ams.2018.712362 On a Certain Representation in the Pairs of ormed Spaces Ahiro Hoshida
More informationSecure Weakly Convex Domination in Graphs
Applied Mathematical Sciences, Vol 9, 2015, no 3, 143-147 HIKARI Ltd, wwwm-hikaricom http://dxdoiorg/1012988/ams2015411992 Secure Weakly Convex Domination in Graphs Rene E Leonida Mathematics Department
More informationIterative Methods for Single Variable Equations
International Journal of Mathematical Analysis Vol 0, 06, no 6, 79-90 HII Ltd, wwwm-hikaricom http://dxdoiorg/0988/ijma065307 Iterative Methods for Single Variable Equations Shin Min Kang Department of
More informationβ Baire Spaces and β Baire Property
International Journal of Contemporary Mathematical Sciences Vol. 11, 2016, no. 5, 211-216 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijcms.2016.612 β Baire Spaces and β Baire Property Tugba
More informationRestrained Independent 2-Domination in the Join and Corona of Graphs
Applied Mathematical Sciences, Vol. 11, 2017, no. 64, 3171-3176 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ams.2017.711343 Restrained Independent 2-Domination in the Join and Corona of Graphs
More informationLinearization of Two Dimensional Complex-Linearizable Systems of Second Order Ordinary Differential Equations
Applied Mathematical Sciences, Vol. 9, 2015, no. 58, 2889-2900 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2015.4121002 Linearization of Two Dimensional Complex-Linearizable Systems of
More informationMorera s Theorem for Functions of a Hyperbolic Variable
Int. Journal of Math. Analysis, Vol. 7, 2013, no. 32, 1595-1600 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2013.212354 Morera s Theorem for Functions of a Hyperbolic Variable Kristin
More informationExact Solutions for a Fifth-Order Two-Mode KdV Equation with Variable Coefficients
Contemporary Engineering Sciences, Vol. 11, 2018, no. 16, 779-784 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ces.2018.8262 Exact Solutions for a Fifth-Order Two-Mode KdV Equation with Variable
More informationThe EM Algorithm for the Finite Mixture of Exponential Distribution Models
Int. J. Contemp. Math. Sciences, Vol. 9, 2014, no. 2, 57-64 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijcms.2014.312133 The EM Algorithm for the Finite Mixture of Exponential Distribution
More informationA Note of the Strong Convergence of the Mann Iteration for Demicontractive Mappings
Applied Mathematical Sciences, Vol. 10, 2016, no. 6, 255-261 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2016.511700 A Note of the Strong Convergence of the Mann Iteration for Demicontractive
More informationDiameter of the Zero Divisor Graph of Semiring of Matrices over Boolean Semiring
International Mathematical Forum, Vol. 9, 2014, no. 29, 1369-1375 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/imf.2014.47131 Diameter of the Zero Divisor Graph of Semiring of Matrices over
More informationOn a 3-Uniform Path-Hypergraph on 5 Vertices
Applied Mathematical Sciences, Vol. 10, 2016, no. 30, 1489-1500 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2016.512742 On a 3-Uniform Path-Hypergraph on 5 Vertices Paola Bonacini Department
More informationThe Modified Adomian Decomposition Method for. Solving Nonlinear Coupled Burger s Equations
Nonlinear Analysis and Differential Equations, Vol. 3, 015, no. 3, 111-1 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.1988/nade.015.416 The Modified Adomian Decomposition Method for Solving Nonlinear
More informationOn the Computation of the Adjoint Ideal of Curves with Ordinary Singularities
Applied Mathematical Sciences Vol. 8, 2014, no. 136, 6805-6812 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2014.49697 On the Computation of the Adjoint Ideal of Curves with Ordinary Singularities
More informationCommon Fixed Point Theorems of Generalized Contractive Mappings Using Weak Reciprocal Continuity
Int. Journal of Math. Analysis, Vol. 8, 204, no. 2, 07-026 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/0.2988/ijma.204.4369 Common Fixed Point Theorems of Generalized Contractive Mappings Using Weak
More informationFuzzy Sequences in Metric Spaces
Int. Journal of Math. Analysis, Vol. 8, 2014, no. 15, 699-706 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2014.4262 Fuzzy Sequences in Metric Spaces M. Muthukumari Research scholar, V.O.C.
More informationRiesz Representation Theorem on Generalized n-inner Product Spaces
Int. Journal of Math. Analysis, Vol. 7, 2013, no. 18, 873-882 HIKARI Ltd, www.m-hikari.com Riesz Representation Theorem on Generalized n-inner Product Spaces Pudji Astuti Faculty of Mathematics and Natural
More informationFixed Point Results in Dislocated Quasi Metric Spaces
International Mathematical Forum, Vol. 9, 2014, no. 14, 677-682 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/imf.2014.4226 Fixed Point Results in Dislocated Quasi Metric Spaces Mujeeb Ur Rahman
More informationON q-analgue OF THE TWISTED L-FUNCTIONS AND q-twisted BERNOULLI NUMBERS. Yilmaz Simsek
J. Korean Math. Soc. 40 (2003), No. 6, pp. 963 975 ON q-analgue OF THE TWISTED L-FUNCTIONS AND q-twisted BERNOULLI NUMBERS Yilmaz Simsek Abstract. The aim of this work is to construct twisted q-l-series
More informationSolution of Differential Equations of Lane-Emden Type by Combining Integral Transform and Variational Iteration Method
Nonlinear Analysis and Differential Equations, Vol. 4, 2016, no. 3, 143-150 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/nade.2016.613 Solution of Differential Equations of Lane-Emden Type by
More informationFinite Groups with ss-embedded Subgroups
International Journal of Algebra, Vol. 11, 2017, no. 2, 93-101 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ija.2017.7311 Finite Groups with ss-embedded Subgroups Xinjian Zhang School of Mathematical
More informationA Generalized Fermat Equation with an Emphasis on Non-Primitive Solutions
International Mathematical Forum, Vol. 12, 2017, no. 17, 835-840 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/imf.2017.78701 A Generalized Fermat Equation with an Emphasis on Non-Primitive Solutions
More informationA Direct Proof of Caristi s Fixed Point Theorem
Applied Mathematical Sciences, Vol. 10, 2016, no. 46, 2289-2294 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2016.66190 A Direct Proof of Caristi s Fixed Point Theorem Wei-Shih Du Department
More informationRemark on a Couple Coincidence Point in Cone Normed Spaces
International Journal of Mathematical Analysis Vol. 8, 2014, no. 50, 2461-2468 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2014.49293 Remark on a Couple Coincidence Point in Cone Normed
More informationOn the New q-extension of Frobenius-Euler Numbers and Polynomials Arising from Umbral Calculus
Adv. Studies Theor. Phys., Vo. 7, 203, no. 20, 977-99 HIKARI Ltd, www.m-hiari.com http://dx.doi.org/0.2988/astp.203.390 On the New -Extension of Frobenius-Euer Numbers and Poynomias Arising from Umbra
More informationSums of Tribonacci and Tribonacci-Lucas Numbers
International Journal of Mathematical Analysis Vol. 1, 018, no. 1, 19-4 HIKARI Ltd, www.m-hikari.com https://doi.org/10.1988/ijma.018.71153 Sums of Tribonacci Tribonacci-Lucas Numbers Robert Frontczak
More informationDouble Contraction in S-Metric Spaces
International Journal of Mathematical Analysis Vol. 9, 2015, no. 3, 117-125 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ijma.2015.1135 Double Contraction in S-Metric Spaces J. Mojaradi Afra
More informationRainbow Connection Number of the Thorn Graph
Applied Mathematical Sciences, Vol. 8, 2014, no. 128, 6373-6377 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ams.2014.48633 Rainbow Connection Number of the Thorn Graph Yixiao Liu Department
More informationParallel Properties of Poles of. Positive Functions and those of. Discrete Reactance Functions
International Journal of Mathematical Analysis Vol. 11, 2017, no. 24, 1141-1150 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ima.2017.77106 Parallel Properties of Poles of Positive Functions and
More informationKKM-Type Theorems for Best Proximal Points in Normed Linear Space
International Journal of Mathematical Analysis Vol. 12, 2018, no. 12, 603-609 HIKARI Ltd, www.m-hikari.com https://doi.org/10.12988/ijma.2018.81069 KKM-Type Theorems for Best Proximal Points in Normed
More informationFixed Point Theorems for Modular Contraction Mappings on Modulared Spaces
Int. Journal of Math. Analysis, Vol. 7, 2013, no. 20, 965-972 HIKARI Ltd, www.m-hikari.com Fixed Point Theorems for Modular Contraction Mappings on Modulared Spaces Mariatul Kiftiah Dept. of Math., Tanjungpura
More informationTwo Constants of Motion in the Generalized Damped Oscillator
Advanced Studies in Theoretical Physics Vol. 10, 2016, no. 2, 57-65 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/astp.2016.511107 Two Constants o Motion in the Generalized Damped Oscillator
More informationHyperbolic Functions and. the Heat Balance Integral Method
Nonl. Analysis and Differential Equations, Vol. 1, 2013, no. 1, 23-27 HIKARI Ltd, www.m-hikari.com Hyperbolic Functions and the Heat Balance Integral Method G. Nhawu and G. Tapedzesa Department of Mathematics,
More informationBlock-Transitive 4 (v, k, 4) Designs and Suzuki Groups
International Journal of Algebra, Vol. 10, 2016, no. 1, 27-32 HIKARI Ltd, www.m-hikari.com http://dx.doi.org/10.12988/ija.2016.51277 Block-Transitive 4 (v, k, 4) Designs and Suzuki Groups Shaojun Dai Department
More informationA Note on Multiplicity Weight of Nodes of Two Point Taylor Expansion
Applied Mathematical Sciences, Vol, 207, no 6, 307-3032 HIKARI Ltd, wwwm-hikaricom https://doiorg/02988/ams2077302 A Note on Multiplicity Weight of Nodes of Two Point Taylor Expansion Koichiro Shimada
More informationSome Reviews on Ranks of Upper Triangular Block Matrices over a Skew Field
International Mathematical Forum, Vol 13, 2018, no 7, 323-335 HIKARI Ltd, wwwm-hikaricom https://doiorg/1012988/imf20188528 Some Reviews on Ranks of Upper Triangular lock Matrices over a Skew Field Netsai
More informationThe Greatest Common Divisor of k Positive Integers
International Mathematical Forum, Vol. 3, 208, no. 5, 25-223 HIKARI Ltd, www.m-hiari.com https://doi.org/0.2988/imf.208.822 The Greatest Common Divisor of Positive Integers Rafael Jaimczu División Matemática,
More information