Turkish Journal of Analysis and Number Theory

ISSN (Print): 2333-1100

ISSN (Online): 2333-1232

Frequency: bimonthly

Editor-in-Chief: Mehmet Acikgoz, Feng Qi, Cenap ozel

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

   

Article

p-Adic Number Fields Acting On W*-Probability Spaces

1Department of Mathematics, 421 Ambrose Hall, Saint Ambrose University, 518 W. Locust St., Davenport, Iowa, 52803, U. S. A.


Turkish Journal of Analysis and Number Theory. 2017, 5(2), 31-56
doi: 10.12691/tjant-5-2-2
Copyright © 2017 Science and Education Publishing

Cite this paper:
Ilwoo Cho. p-Adic Number Fields Acting On W*-Probability Spaces. Turkish Journal of Analysis and Number Theory. 2017; 5(2):31-56. doi: 10.12691/tjant-5-2-2.

Correspondence to: Ilwoo  Cho, Department of Mathematics, 421 Ambrose Hall, Saint Ambrose University, 518 W. Locust St., Davenport, Iowa, 52803, U. S. A.. Email: choilwoo@sau.edu

Abstract

In this paper, we study how a p-adic number field acts on an arbitrarily fixed W*-algebra, and how it affects the original free-probabilistic information on the W*-algebra, for each prime p. In particular, by understanding the σ-algebra of as a semigroup equipped with the setintersection, we act on a unital tracial W*-probability space (M,tr), creating the corresponding semigroup W*-dynamical system. From such a dynamical system, construct the crossed product W*-algebra equipped with a suitable linear functional. We study free probability on such W*-dynamical operator-algebraic structures determined by primes, and those on corresponding free products of such structures over primes. As application, we study cases where given W*-probability spaces are generated by countable discrete groups.

Keywords

References

[1]  I. Cho, Free Product C*-Algebras Induced by *-Algebras over p-Adic Number Fields for Primes p, (2016). Submitted to J. Numb. Theo. Anal. Acad.
 
[2]  I. Cho, Semicircular Elements Induced by p-Adic Number Fields, (2016). Submitted to Adv. Oper. Theo.
 
[3]  I. Cho, On Dynamical Systems Induced by p-Adic Number Fields, Opuscula Math., 35, no. 4, (2015). 445-484.
 
[4]  I. Cho, Free-Distributional Data of Arithmetic Functions and Corresponding Generating Functions Determined by Gaps of Primes, Compl. Anal. Oper. Theo., vol 8, issue 2, (2014). 537-570.
 
[5]  I. Cho, Classification of Arithmetic Functions and Corresponding Free-Moment L-Functions, Bull. Korean Math. Soc., 52, no. 3, (2015). 717-734.
 
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[6]  I. Cho, Dynamical Systems on Arithmetic Functions Determined by Prims, Banach J. Math. Anal., 9, no. 1, (2015). 173-215.
 
[7]  I. Cho, and T. Gillespie, Free Probability on the Hecke Algebra, Compl. Anal. Oper. Theo., (2014).
 
[8]  I. Cho, and P. E. T. Jorgensen, Krein-Space Operators Induced by Dirichlet Characters, Special Issues: Contemp. Math.: Commutative and Noncommutative Harmonic Analysis and Applications, Amer. Math. Soc., (2014) 3-33.
 
[9]  T. Gillespie, Superposition of Zeroes of Automorphic L-Functions and Functoriality, Univ. of Iowa, (2010). PhD Thesis.
 
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Article

Fixed Point Theorems for Expansive Mappings in G-metric Spaces

1Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan


Turkish Journal of Analysis and Number Theory. 2017, 5(2), 57-62
doi: 10.12691/tjant-5-2-3
Copyright © 2017 Science and Education Publishing

Cite this paper:
Rahim Shah, Akbar Zada. Fixed Point Theorems for Expansive Mappings in G-metric Spaces. Turkish Journal of Analysis and Number Theory. 2017; 5(2):57-62. doi: 10.12691/tjant-5-2-3.

Correspondence to: Rahim  Shah, Department of Mathematics, University of Peshawar, Peshawar 25000, Pakistan. Email: safeer_rahim@yahoo.com, rahimshahstd@upesh.edu.pk

Abstract

In this paper we prove some fixed point theorems for contractive as well as for expansive mappings in G-metric space by using integral type contraction. Finally, we present an example.

Keywords

References

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Article

Some New Integral Inequalities for -Times Differentiable - Convex Functions in the First Sense

1Department of Mathematics, Faculty of Sciences and Arts, Giresun University-Giresun-TÜRKİYE

2Institute of Science, Ordu University-Ordu-TÜRKİYE


Turkish Journal of Analysis and Number Theory. 2017, 5(2), 63-68
doi: 10.12691/tjant-5-2-4
Copyright © 2017 Science and Education Publishing

Cite this paper:
Mahir Kadakal, Huriye Kadakal, İmdat İşcan. Some New Integral Inequalities for -Times Differentiable - Convex Functions in the First Sense. Turkish Journal of Analysis and Number Theory. 2017; 5(2):63-68. doi: 10.12691/tjant-5-2-4.

Correspondence to: Mahir  Kadakal, Department of Mathematics, Faculty of Sciences and Arts, Giresun University-Giresun-TÜRKİYE. Email: mahirkadakal@gmail.com

Abstract

In this work, by using an integral identity together with both the Hölder and the Power-Mean integral inequality we establish several new inequalities for n-time differentiable -convex functions in the first sense.

Keywords

References

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[5]  S. S. Dragomir and C. E. M. Pearce, “Selected Topics on Hermite-Hadamard Inequalities and Applications”, RGMIA Monographs, Victoria University, 2000.
 
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[20]  S. Maden, H. Kadakal, M. Kadakal and İ. İşcan, “Some new integral inequalities for n-times differentiable convex and concave functions”. https://www.researchgate.net/publication/312529563, (Submitted)
 
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