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Article

On the Moments of the Function E*(t)

1Aleksandar Ivić, Katedra Matematike RGF-A, Universitet U Beogradu, Ðušina, Beograd, Serbia


Turkish Journal of Analysis and Number Theory. 2014, 2(3), 102-109
DOI: 10.12691/tjant-2-3-9
Copyright © 2014 Science and Education Publishing

Cite this paper:
Aleksandar Ivić. On the Moments of the Function E*(t). Turkish Journal of Analysis and Number Theory. 2014; 2(3):102-109. doi: 10.12691/tjant-2-3-9.

Correspondence to: Aleksandar  Ivić, Aleksandar Ivić, Katedra Matematike RGF-A, Universitet U Beogradu, Ðušina, Beograd, Serbia. Email: ivic@rgf.bg.ac.rs, aivic2000@yahoo.com

Abstract

Let denote the error term in the Dirichlet divisor problem, and the error term in the asymptotic formula for the mean square of If with then we discuss bounds for third, fourth and fifth power moment of We also prove that always changes sign in for and obtain (conditionally) the existence of its large positive, or small negative values.

Keywords

References

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[[3]  A. Ivić, Large values of the error term in the divisor problem, Inventiones Math. 71(1983), 513-520.
 
[[4]  A. Ivić, The Riemann zeta-function, John Wiley & Sons, New York, 1985 (2nd ed. Dover, Mineola, New York, 2003).
 
[[5]  A. Ivić, The mean values of the Riemann zeta-function, LNs 82, Tata Inst. of Fundamental Research, Bombay (distr. by Springer Verlag, Berlin etc.), 1991.
 
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[6]  A. Ivić, On the Riemann zeta-function and the divisor problem, Central European J. Math. (2)(4) (2004), 1-15; II, ibid. (3)(2) (2005), 203-214; III, Annales Univ. Sci. Budapest, Sect. Comp. 29(2008), 3-23.; IV, Uniform Distribution Theory 1(2006), 125-135.
 
[7]  A. Ivić, On the mean square of the zeta-function and the divisor problem, Annales Acad. Scien. Fennicae Mathematica 23(2007), 1-9.
 
[8]  A. Ivić, Some remarks on the moments of |(ζ(1/2+ it)| in short intervals, Acta Math. Hung. 119(2008), 15-24.
 
[9]  A. Ivić, On some mean square estimates for the zeta-function in short intervals, Annales Univ. Sci. Budapest., Sect. Comp. 40(2013), 321-335.
 
[10]  A. Ivić, On some mean value results for the zeta-function in short intervals, Acta Arith. 162.2(2014), 141-158.
 
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Article

Some Inequalities for the Generalized Trigonometric and Hyperbolic Functions

1Department of Mathematics, Binzhou University, Binzhou City, Shandong Province, China

2College of Mathematics, Inner Mongolia University for Nationalities, Tongliao City, Inner Mongolia Autonomous Region, China

3Department of Mathematics, College of Science, Tianjin Polytechnic University, Tianjin City, China;Institute of Mathematics, Henan Polytechnic University, Jiaozuo City, Henan Province, China


Turkish Journal of Analysis and Number Theory. 2014, 2(3), 96-101
DOI: 10.12691/tjant-2-3-8
Copyright © 2014 Science and Education Publishing

Cite this paper:
Li Yin, Li-Guo Huang, and Feng Qi. Some Inequalities for the Generalized Trigonometric and Hyperbolic Functions. Turkish Journal of Analysis and Number Theory. 2014; 2(3):96-101. doi: 10.12691/tjant-2-3-8.

Correspondence to: Li  Yin, Department of Mathematics, Binzhou University, Binzhou City, Shandong Province, China. Email: yinli_79@163.com

Abstract

In the paper, the authors establish some inequalities of the generalized trigono-metric and hyperbolic functions, partially solve a conjecture posed by R. Klén, M. Vuorinen, and X.-H. Zhang, and finally pose an open problem.

Keywords

References

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[[3]  B. A. Bhayo and M. Vuorinen, On generalized trigonometric functions with two parameters, J. Approx. Theory 164 (2012), no. 10, 1415-1426.
 
[[4]  B. A. Bhayo and M. Vuorinen, Power mean inequality of generalized trigonometric functions, available online at http://arxiv.org/abs/1209.0873.
 
[[5]  B. C. Carlson, Special Functions of Applied Mathematics, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1977.
 
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[6]  D. E. Edmundes, P. Gurka, and J. Lang, Properties of generalized trigonometric functions, J. Approx. Theory 164 (2012), no. 1, 47-56.
 
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[8]  R. Klén, M. Vuorinen, and X.-H. Zhang, Inequali ties for the generalized trigonometric and hyperbolic functions, J. Math. Anal. Appl. 409 (2014), no. 1, 521-529.
 
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Article

New Properties for The Ramanujan’S Continued Fraction of Order 12

1Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysore 570 006, INDIA


Turkish Journal of Analysis and Number Theory. 2014, 2(3), 90-95
DOI: 10.12691/tjant-2-3-7
Copyright © 2014 Science and Education Publishing

Cite this paper:
Chandrashekar Adiga, M. S. Surekha, A. Vanitha. New Properties for The Ramanujan’S Continued Fraction of Order 12. Turkish Journal of Analysis and Number Theory. 2014; 2(3):90-95. doi: 10.12691/tjant-2-3-7.

Correspondence to: Chandrashekar  Adiga, Department of Studies in Mathematics, University of Mysore, Manasagangotri, Mysore 570 006, INDIA. Email: c_adiga@hotmail.com

Abstract

In this paper, we derive new identities involving a continued fraction of Ramanujan of order twelve that are similar to those of the Ramanujan-Göllnitz-Gordon continued fraction.

Keywords

References

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Article

On The Hermite- Hadamard-Fejér Type Integral Inequality for Convex Function

1Department of Mathematics, Faculty of Science and Arts, Düzce University, Konu-ralp Campus, Düzce-TURKEY

2Department of Mathematics, Faculty of Science, Bartn University, Konuralp Cam-pus, BARTIN-TURKEY


Turkish Journal of Analysis and Number Theory. 2014, 2(3), 85-89
DOI: 10.12691/tjant-2-3-6
Copyright © 2014 Science and Education Publishing

Cite this paper:
Mehmet Zeki Sarikaya, Samet Erden. On The Hermite- Hadamard-Fejér Type Integral Inequality for Convex Function. Turkish Journal of Analysis and Number Theory. 2014; 2(3):85-89. doi: 10.12691/tjant-2-3-6.

Correspondence to: Mehmet  Zeki Sarikaya, Department of Mathematics, Faculty of Science and Arts, Düzce University, Konu-ralp Campus, Düzce-TURKEY. Email: sarikayamz@gmail.com

Abstract

In this paper, we extend some estimates of the right hand side of a Hermite- Hadamard-Fejér type inequality for functions whose first derivatives absolute values are convex. The results presented here would provide extensions of those given in earlier works.

Keywords

References

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[6]  M. E. Kiris and M. Z. Sarikaya, On the new generalization of Ostrowski type inequality for double integrals, International Journal of Modern Mathematical Sciences, 2014, 9 (3): 221-229.
 
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Article

On an Inequality of Ostrowski Type via Variant of Pompeiu's Mean Value Theorem

1Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Turkey


Turkish Journal of Analysis and Number Theory. 2014, 2(3), 80-84
DOI: 10.12691/tjant-2-3-5
Copyright © 2014 Science and Education Publishing

Cite this paper:
Mehmet Zeki SARIKAYA, Hüseyin BUDAK. On an Inequality of Ostrowski Type via Variant of Pompeiu's Mean Value Theorem. Turkish Journal of Analysis and Number Theory. 2014; 2(3):80-84. doi: 10.12691/tjant-2-3-5.

Correspondence to: Mehmet  Zeki SARIKAYA, Department of Mathematics, Faculty of Science and Arts, Düzce University, Düzce, Turkey. Email: sarikayamz@gmail.com

Abstract

The main of this paper is to establish an Ostrowski type inequality for two variables functions by using a mean value theorem.

Keywords

References

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[[2]  S.S. Dragomir, An inequality of Ostrowski type via Pompeiu's mean value theorem, J. of Inequal. in Pure and Appl. Math., 6(3) (2005), Art. 83.
 
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[[4]  P.P Pecaric and S. Ungar, On an inequality of Ostrowski type, J. of Inequal. in Pure and Appl. Math., 7(4) (2006), Art. 151.
 
[[5]  E. C. Popa, An inequality of Ostrowski type via a mean value theorem, General Mathematics Vol. 15, No. 1, 2007, 93-100.
 
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[6]  D. Pompeiu, Sur une proposition analogue au théorème des accroissements finis, Mathematica (Cluj, Romania), 22 (1946), 143-146.
 
[7]  A. Ostrowski, Uber die Absolutabweichung einer differentierbaren Funktionen von ihrem Integralmittelwert, Comment. Math. Helv., 10(1938), 226-227.
 
[8]  F. Ahmad, N. A. Mir and M.Z. Sarikaya, An inequality of Ostrowski type via variant of Pompeiu's mean value theorem, J. Basic. Appl. Sci. Res., 4(4)204-211, 2014.
 
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Article

Using Area Mean Value Theorem to Solve Some Double Integrals

1Department of Management and Information, Nan Jeon University of Science and Technology, Tainan City, Taiwan

2Department of Information Technology, Nan Jeon University of Science and Technology, Tainan City, Taiwan


Turkish Journal of Analysis and Number Theory. 2014, 2(3), 75-79
DOI: 10.12691/tjant-2-3-4
Copyright © 2014 Science and Education Publishing

Cite this paper:
Chii-Huei Yu, Shinn-Der Sheu. Using Area Mean Value Theorem to Solve Some Double Integrals. Turkish Journal of Analysis and Number Theory. 2014; 2(3):75-79. doi: 10.12691/tjant-2-3-4.

Correspondence to: Chii-Huei  Yu, Department of Management and Information, Nan Jeon University of Science and Technology, Tainan City, Taiwan. Email: chiihuei@nju.edu.tw

Abstract

The present paper studies six types of double integrals and uses Maple for verification. These double integrals can be solved using area mean value theorem. On the other hand, some examples are used to demonstrate the calculations.

Keywords

References

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[[4]  C. -H. Yu, “A study of two types of definite integrals with Maple,” Jökull Journal, Vol. 64, No. 2, pp. 543-550, 2014.
 
[[5]  C. -H. Yu, “Evaluating two types of definite integrals using Parseval’s theorem,” Wulfenia Journal, Vol. 21, No. 2, pp. 24-32, 2014.
 
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[6]  C. -H. Yu, “Solving some definite integrals using Parseval’s theorem,” American Journal of Numerical Analysis, Vol. 2, No. 2, pp. 60-64, 2014.
 
[7]  C. -H. Yu, “Some types of integral problems,” American Journal of Systems and Software, Vol. 2, No. 1, pp. 22-26, 2014.
 
[8]  C. -H. Yu, “Using Maple to study the double integral problems,” Applied and Computational Mathematics, Vol. 2, No. 2, pp. 28-31, 2013.
 
[9]  C. -H. Yu, “A study on double Integrals,” International Journal of Research in Information Technology, Vol. 1, Issue. 8, pp. 24-31, 2013.
 
[10]  C. -H. Yu, “Application of Parseval’s theorem on evaluating some definite integrals,” Turkish Journal of Analysis and Number Theory, Vol. 2, No. 1, pp. 1-5, 2014.
 
[11]  C. -H. Yu, “Evaluation of two types of integrals using Maple, ”Universal Journal of Applied Science, Vol. 2, No. 2, pp. 39-46, 2014.
 
[12]  C. -H. Yu, “Studying three types of integrals with Maple, ”American Journal of Computing Research Repository, Vol. 2, No. 1, pp. 19-21, 2014.
 
[13]  C. -H. Yu, “The application of Parseval’s theorem to integral problems,” Applied Mathematics and Physics, Vol. 2, No. 1, pp. 4-9, 2014.
 
[14]  C. -H. Yu, “A study of some integral problems using Maple,” Mathematics and Statistics, Vol. 2, No. 1, pp. 1-5, 2014.
 
[15]  C. -H. Yu, “Solving some definite integrals by using Maple, ”World Journal of Computer Application and Technology, Vol. 2, No. 3, pp. 61-65, 2014.
 
[16]  C. -H. Yu, “Using Maple to study two types of integrals,” International Journal of Research in Computer Applications and Robotics, Vol. 1, Issue. 4, pp. 14-22, 2013.
 
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[26]  C. -H. Yu, “Application of Maple on some type of integral problem,”(in Chinese) Proceedings of the Ubiquitous-Home Conference 2012, Taiwan, pp.206-210, 2012.
 
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Article

Numerical Computation Based on the Method of Fundamental Solutions for a Cauchy Problem of Heat Equation

1School of Mathematics and Computer science, Shanxi Normal University, Linfen, China


Turkish Journal of Analysis and Number Theory. 2014, 2(3), 70-74
DOI: 10.12691/tjant-2-3-3
Copyright © 2014 Science and Education Publishing

Cite this paper:
Ruihua Cao. Numerical Computation Based on the Method of Fundamental Solutions for a Cauchy Problem of Heat Equation. Turkish Journal of Analysis and Number Theory. 2014; 2(3):70-74. doi: 10.12691/tjant-2-3-3.

Correspondence to: Ruihua  Cao, School of Mathematics and Computer science, Shanxi Normal University, Linfen, China. Email: caoruihua0056@126.com

Abstract

In this note, a boundary integral equation method coupled with the method of fundamental solutions for solving an inverse heat conduction problem is considered. The Tikhonov regularization method is employed for solving this system of equations. Determination of regularization parameter is based on GCV criterion. To illustrate our main results, some numerical examples are given.

Keywords

References

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Article

A Note on Saigo’s Fractional Integral Inequalities

1School of Mathematics and Computer Science, Shanxi Normal University, Linfen, Shanxi, People’s Republic of China

2Department of Mathematics, Amity University, Jaipur, India

3Department of Basic Sciences (Mathematics), College of Technology and Engineering, M.P. University of Agriculture and Technology, Udaipur, India

4Department of Civil Engineering, College of Technology and Engineering, M.P. University of Agriculture and Technology, Udaipur, India


Turkish Journal of Analysis and Number Theory. 2014, 2(3), 65-69
DOI: 10.12691/tjant-2-3-2
Copyright © 2014 Science and Education Publishing

Cite this paper:
Guotao Wang, Harshvardhan Harsh, S.D. Purohit, Trilok Gupta. A Note on Saigo’s Fractional Integral Inequalities. Turkish Journal of Analysis and Number Theory. 2014; 2(3):65-69. doi: 10.12691/tjant-2-3-2.

Correspondence to: Guotao  Wang, School of Mathematics and Computer Science, Shanxi Normal University, Linfen, Shanxi, People’s Republic of China. Email: wgt2512@163.com

Abstract

In this paper, some new integral inequalities related to the bounded functions, involving Saigo’s fractional integral operators, are eshtablished. Special cases of the main results are also pointed out.

Keywords

References

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Article

Integral Inequalities of Hermite–Hadamard Type for m-AH Convex Functions

1College of Mathematics, Inner Mongolia University for Nationalities, Tongliao City, Inner Mongolia Autonomous Region, China

2Department of Mathematics, School of Science, Tianjin Polytechnic University, Tianjin City, China

3Institute of Mathematics, Henan Polytechnic University, jiaozuo City, Henan Province, China


Turkish Journal of Analysis and Number Theory. 2014, 2(3), 60-64
DOI: 10.12691/tjant-2-3-1
Copyright © 2014 Science and Education Publishing

Cite this paper:
Tian-Yu Zhang, Feng Qi. Integral Inequalities of Hermite–Hadamard Type for m-AH Convex Functions. Turkish Journal of Analysis and Number Theory. 2014; 2(3):60-64. doi: 10.12691/tjant-2-3-1.

Correspondence to: Tian-Yu  Zhang, College of Mathematics, Inner Mongolia University for Nationalities, Tongliao City, Inner Mongolia Autonomous Region, China. Email: zhangtianyu7010@126.com

Abstract

In the paper, the authors introduce the concept “m-AH convex functions” and establish some inequalities of Hermite-Hadamard type for m-AH convex functions.

Keywords

References

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