American Journal of Mathematical Analysis

ISSN (Print): 2333-8490

ISSN (Online): 2333-8431

Website: http://www.sciepub.com/journal/AJMA

Current Issue» Volume 3, Number 1 (2015)

Article

On the Analytic Curve of C2 which is not Omitted by Every Fatou-Bieberbach Domain

1Yukinobu Adachi, Kurakuen, Nishinomiya, Hyogo, Japan


American Journal of Mathematical Analysis. 2015, 3(1), 19-20
DOI: 10.12691/ajma-3-1-4
Copyright © 2015 Science and Education Publishing

Cite this paper:
YUKINOBU ADACHI. On the Analytic Curve of C2 which is not Omitted by Every Fatou-Bieberbach Domain. American Journal of Mathematical Analysis. 2015; 3(1):19-20. doi: 10.12691/ajma-3-1-4.

Correspondence to: YUKINOBU  ADACHI, Yukinobu Adachi, Kurakuen, Nishinomiya, Hyogo, Japan. Email: fwjh5864@nifty.com

Abstract

Let C be an irreducible (may be transendental) analytic curve whose genus is geater than 1. Then every Fatou-Bieberbach domain does not omit C.

Keywords

References

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Article

Two Operator Representations for the Trivariate q-Polynomials and Hahn Polynomials

1Department of Mathematics, College of Education for Pure Sciences, Thi-Qar University, Thi-Qar, Iraq


American Journal of Mathematical Analysis. 2015, 3(1), 10-18
DOI: 10.12691/ajma-3-1-3
Copyright © 2015 Science and Education Publishing

Cite this paper:
Mohammed A. Abdlhusein. Two Operator Representations for the Trivariate q-Polynomials and Hahn Polynomials. American Journal of Mathematical Analysis. 2015; 3(1):10-18. doi: 10.12691/ajma-3-1-3.

Correspondence to: Mohammed  A. Abdlhusein, Department of Mathematics, College of Education for Pure Sciences, Thi-Qar University, Thi-Qar, Iraq. Email: mmhd122@yahoo.com

Abstract

In this paper we introduce a trivariate q-polynomials Fn(x, y, z; q) as a general form of Hahn polynomials and . We represent Fn(x, y, z; q) by two operators: the homogeneous q-shift operator L(xy) given by H. L. Saad and A. A. Sukhi [16], and the Cauchy companian operator E(a, b; θ) given by V. Y. B. Chen [8] to derive the generating function, symmetric property, Mehler’s formula, Rogers formula, another Roger-type formula, linearization formula and an extended Rogers formula for the trivariate q-polynomials. Then we give the corresponding formulas for both Hahn polynomials and by represent Hahn polynomials by the operators L(xy) and E(a, b; θ), also by a special substitution in the trivariate q-polynomials Fn(x, y, z; q).

Keywords

References

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15]  H. L. Saad and M. A. Abdlhusein, The q-exponential operator and generalized Rogers-Szeg¨o polynomials, Journal of Advances in Mathematics, 8 (2014) 1440-1455.
 
16]  H. L. Saad and A. A. Sukhi, Another homogeneous q-difference operator, Applied Mathematics and Computation 215 (2010) 4332-4339.
 
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Article

Common Fixed Point Theorems for Two Self-maps in Cone Metric Spaces under Different Contractive Conditions

1Department of Mathematics, University College of Science, Osmania University, Hyderabad, India


American Journal of Mathematical Analysis. 2015, 3(1), 5-9
DOI: 10.12691/ajma-3-1-2
Copyright © 2015 Science and Education Publishing

Cite this paper:
P. Rama Bhadra Murthy, M. Rangamma. Common Fixed Point Theorems for Two Self-maps in Cone Metric Spaces under Different Contractive Conditions. American Journal of Mathematical Analysis. 2015; 3(1):5-9. doi: 10.12691/ajma-3-1-2.

Correspondence to: P.  Rama Bhadra Murthy, Department of Mathematics, University College of Science, Osmania University, Hyderabad, India. Email: badri2502@gmail.com

Abstract

The existence of unique common fixed point theorems for two weakly compatible self-maps satisfying different contractive conditions in cone metric spaces without using normality.

Keywords

References

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Article

Inequalities for the Sth Derivative of Polynomials Not Vanishing inside A Circle

1Govt. Department of Education Jammu and Kashmir, India


American Journal of Mathematical Analysis. 2015, 3(1), 1-4
DOI: 10.12691/ajma-3-1-1
Copyright © 2015 Science and Education Publishing

Cite this paper:
GULSHAN SINGH. Inequalities for the Sth Derivative of Polynomials Not Vanishing inside A Circle. American Journal of Mathematical Analysis. 2015; 3(1):1-4. doi: 10.12691/ajma-3-1-1.

Correspondence to: GULSHAN  SINGH, Govt. Department of Education Jammu and Kashmir, India. Email: gulshansingh1@rediffmail.com

Abstract

Let P(z) be a polynomial of degree n having all its zeros in , then for , Bidkham and Dewan [J. Math. Anal. Appl. 166(1992), 191-193] proved max In this paper, we prove an interesting generalization as well as an improvement of this result by considering the sth derivative of lacunary type of polynomials P(z) of degree n > 3.

Keywords

References

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