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### Content: Volume 2, Issue 3(Cover Page, Table of Contents)

### Article

**On the Moments of the Function E*(t)**

^{1}Aleksandar 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

*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. | ||

[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. | ||

[11] | M. Jutila, Riemann’s zeta-function and the divisor problem, Arkiv Mat. 21(1983), 75-96 and II, ibid. 31(1993), 61-70. | ||

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### Article

**Some Inequalities for the Generalized Trigonometric and Hyperbolic Functions**

^{1}Department of Mathematics, Binzhou University, Binzhou City, Shandong Province, China

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

^{3}Department 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

### Keywords

### References

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[7] | W.-D. Jiang, M.-K. Wang, Y.-M. Chu, Y.-P. Jiang, and F. Qi, Convexity of the generalized sine function and the generalized hyperbolic sine function, J. Approx. Theory 174 (2013), 1-9. | ||

[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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[11] | E. Neumann and J. Sándor, On some inequalities involving trigonometric and hyperbolic functions with emphasis on the Cusa-Huygens, Wilker, and Huygens inequalities, Math. Inequal. Appl. 13 (2010), no. 4, 715-723. | ||

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### Article

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

^{1}Department 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

### Keywords

### References

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[7] | Boonrod Yuttanan, New properties for the Ramanujan-Göllnitz-Gordon continued fraction, Acta Arithmetric, 151(3) (2012), 293-310. | ||

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[14] | K. R. Vasuki, G. Sharth and K. R. Rajanna, Two modular equations for squares of the cubic functions with applications, Note di Math.30 (2) (2010), 61-70. | ||

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### Article

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

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

^{2}Department 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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[11] | M. Z. Sarikaya, E. Set, H. Yaldiz and N., Basak, Hermite -Hadamard.s inequalities for fractional integrals and related fractional inequalities, Mathematical and Computer Modelling, 57 (2013) 2403. 2407. | ||

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[14] | K-L. Tseng, G-S. Yang and K-C. Hsu, Some inequalities for differentiable mappings and applications to Fejer inequality and weighted trapozidal formula, Taiwanese J. Math. 15 (4), pp: 1737-1747, 2011. | ||

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### Article

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

^{1}Department 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

### Keywords

### References

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[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. | ||

### Article

**Using Area Mean Value Theorem to Solve Some Double Integrals**

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

^{2}Department 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

### Keywords

### References

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[5] | C. -H. Yu, “Evaluating two types of definite integrals using Parseval’s theorem,” Wulfenia Journal, Vol. 21, No. 2, pp. 24-32, 2014. | ||

[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. | ||

[17] | C. -H. Yu, “Solving some integrals with Maple,” International Journal of Research in Aeronautical and Mechanical Engineering, Vol. 1, Issue. 3, pp. 29-35, 2013. | ||

[18] | C. -H. Yu, “A study on integral problems by using Maple,” International Journal of Advanced Research in Computer Science and Software Engineering, Vol. 3, Issue. 7, pp. 41-46, 2013. | ||

[19] | C. -H. Yu, “Evaluating some integrals with Maple,” International Journal of Computer Science and Mobile Computing, Vol. 2, Issue. 7, pp. 66-71, 2013. | ||

[20] | C. -H. Yu, “Application of Maple on evaluation of definite integrals,” Applied Mechanics and Materials, Vols. 479-480 (2014), pp. 823-827, 2013. | ||

[21] | C. -H. Yu, “Application of Maple on the integral problems,” Applied Mechanics and Materials, Vols. 479-480 (2014), pp. 849-854, 2013. | ||

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[32] | T. -J. Chen and C. -H. Yu, “Fourier series expansions of some definite integrals,” Sylwan Journal, Vol. 158, Issue. 5, pp. 124-131, 2014. | ||

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### Article

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

^{1}School 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

### Keywords

### References

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### Article

**A Note on Saigo’s Fractional Integral Inequalities**

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

^{2}Department of Mathematics, Amity University, Jaipur, India

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

^{4}Department 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

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### References

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### Article

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

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

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

^{3}Institute 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

### Keywords

### References

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