Turkish Journal of Analysis and Number Theory

### Content: Volume 2, Issue 3

## Article

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

^{1,}

^{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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## 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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## 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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## 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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## 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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[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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## 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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## Article

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

^{1,}

^{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

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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

## Keywords

## 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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[2] | U.S. Kirmaci, Inequalities for differentiable mappings and applications to special means of real numbers and to midpoint formula, Appl. Math. Comp. 147 (2004), 137-146. | ||

[3] | G. Toader, Some generalizations of the convexity, Proceedings of the Colloquium on Approximation and Optimization, Univ. Cluj-Napoca, Cluj-Napoca, 1985, 329-338. | ||

[4] | S.S. Dragomir, On some new inequalities of Hermite-Hadamard type for m-convex functions, Tamkang J. Math. 33 (2002) 45-55. | ||

[5] | S.S. Dragomir, G. Toader, Some inequalities for m-convex functions, Studia Univ. Babes¸-Bolyai Math. 38 (1993), 21-28. | ||

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10] | S.-H. Wang, B.-Y. Xi, and F. Qi, Some new inequalities of Hermite-Hadamard type for n-time dierentiable functions which are m-convex, Analysis (Munich) 32 (2012), no. 3, 247-262. | ||

11] | B.-Y. Xi, R.-F. Bai, and F. Qi, Hermite-Hadamard type inequalities for the m-and (a,m)-geometrically convex functions, Aequationes Math., 84 (2012), no. 3, 261-269. | ||

12] | V.G. Mihesan. A generalization of the convexity, Seminar on functional equations, approximation and convexity, Cluj-Napoca, 1993. (Romania). | ||

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