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Article

Some Generalized Hermite-Hadamard Type Inequalities for Quasi-Geometrically Convex Functions

1Department of Mathematics, Faculty of Sciences and Arts, Giresun University, Giresun, Turkey


American Journal of Mathematical Analysis. 2013, 1(3), 48-52
DOI: 10.12691/ajma-1-3-5
Copyright © 2013 Science and Education Publishing

Cite this paper:
İmdat İşcan. Some Generalized Hermite-Hadamard Type Inequalities for Quasi-Geometrically Convex Functions. American Journal of Mathematical Analysis. 2013; 1(3):48-52. doi: 10.12691/ajma-1-3-5.

Correspondence to: İmdat  İşcan, Department of Mathematics, Faculty of Sciences and Arts, Giresun University, Giresun, Turkey. Email: imdat.iscan@giresun.edu.tr

Abstract

In this paper, by Hölder’s integral inequality, some new generalized Hermite-Hadamard type integral inequalities for quasi-geometrically convex functions are obtained.

Keywords

References

[[
[[1]  Iscan, I., “Some new Hermite-Hadamard type inequalities for geometrically convex functions”, Mathematics and Statistics, 1 (2). 86-91. 2013.
 
[[2]  Iscan, I., “New general integral inequalities for quasi-geometrically convex functions via fractional integrals”, J. Inequal. Appl., 2013 (491). pp 15. 2013.
 
[[3]  Ji, A.-P., Zhang, T.-Y. and Qi F.,” Integral inequalities of Hermite-Hadamard type for (α,m)-GA-convex functions”. arxiv:1306.0852. Available online at http://arxiv.org/abs/1306.0852.
 
[[4]  Niculescu, C.P., “Convexity according to the geometric mean”, Math. Inequal. Appl., 3 (2). 571-579. 2000.
 
[[5]  Niculescu, C.P., “Convexity according to mean”, Math. Inequal. Appl.,6 (4). 155-167. 2003. http://dx.doi.org/10.7153/mia-03-19.
 
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[6]  Park, J., “Some generalized inequalities of Hermite-Hadamard type for (α,m)-geometric-arithmetically convex functions, Applied Mathematical Sciences, 7 (95). 4743-4759. 2013.
 
[7]  Zhang, T.-Y., Ji, A.-P. and Qi, F., “Some inequalities of Hermite-Hadamard type for GA-convex functions with applications to means”, Le Mathematiche, LXVIII (I). 229-239. 2013.
 
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Article

Summability of a Jacobi Series by Lower Triangular Matrix Method

1Tribhuvan University, Nepal


American Journal of Mathematical Analysis. 2013, 1(3), 42-47
DOI: 10.12691/ajma-1-3-4
Copyright © 2013 Science and Education Publishing

Cite this paper:
Binod Prasad Dhakal. Summability of a Jacobi Series by Lower Triangular Matrix Method. American Journal of Mathematical Analysis. 2013; 1(3):42-47. doi: 10.12691/ajma-1-3-4.

Correspondence to: Binod  Prasad Dhakal, Tribhuvan University, Nepal. Email: binod_dhakal2004@yahoo.com

Abstract

The Jacobi polynomial Pn(α,β)(x) which is obtained from Jacobi differential equation is an orthogonal polynomial over the interval [-1, 1] with respect to weight function (1-x)α(1+x)β, α>-1, β>-1. Here Jacobi series has been taken and established a theorem on lower triangular matrix summability of a Jacobi series.

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References

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[6]  Lal, Shyam: On the degree of approximation of conjugate of function belonging to Weighted W (Lp,ξ(t)) class by matrix summability means of conjugate series of a Fourier series, Tamkang J. Math., 31(4), 279-288. 2004.
 
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Article

g-reciprocal Continuity in Symmetric Spaces

1Applied Science Department, Bipin Tripahti Kumaon Institute of Technology, Almora, India


American Journal of Mathematical Analysis. 2013, 1(3), 39-41
DOI: 10.12691/ajma-1-3-3
Copyright © 2013 Science and Education Publishing

Cite this paper:
Arvind Bhatt. g-reciprocal Continuity in Symmetric Spaces. American Journal of Mathematical Analysis. 2013; 1(3):39-41. doi: 10.12691/ajma-1-3-3.

Correspondence to: Arvind Bhatt, Applied Science Department, Bipin Tripahti Kumaon Institute of Technology, Almora, India. Email: arvindbhu_6june@rediffmail.com

Abstract

In this paper, we obtain a common fixed point theorem by employing the notion of g-reciprocal continuity in symmetric spaces. We demonstrate that g-reciprocal continuity ensures the existence of common fixed point under strict contractive conditions, which otherwise do not ensure the existence of fixed points.

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References

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Article

Hermite-Hadamard’s Inequalities for Preinvex Function via Fractional Integrals and Related Fractional Inequalities

1Department of Mathematics, Faculty of Arts and Sciences, Giresun University, Giresun, Turkey


American Journal of Mathematical Analysis. 2013, 1(3), 33-38
DOI: 10.12691/ajma-1-3-2
Copyright © 2013 Science and Education Publishing

Cite this paper:
İmdat İşcan. Hermite-Hadamard’s Inequalities for Preinvex Function via Fractional Integrals and Related Fractional Inequalities. American Journal of Mathematical Analysis. 2013; 1(3):33-38. doi: 10.12691/ajma-1-3-2.

Correspondence to: İmdat İşcan, Department of Mathematics, Faculty of Arts and Sciences, Giresun University, Giresun, Turkey. Email: imdat.iscan@giresun.edu.tr

Abstract

In this paper, the author has established Hermite- Hadamard’s inequalities for preinvex functions and has extended some estimates of the right side of a Hermite- Hadamard type inequalities for preinvex functions via fractional integrals.

Keywords

References

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[8]  Iscan, I., “New estimates on generalization of some integral inequalities for s-convex functions and their applications,” International Journal of Pure and Applied Mathematics, 86 (4). 727-746. 2013.
 
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Article

The (G’/G)-Expansion Method and Traveling Wave Solutions for Some Nonlinear PDEs

1Mathematics Department, Faculty of Science, Taif University, Kingdom of Saudi Arabia


American Journal of Mathematical Analysis. 2013, 1(3), 28-32
DOI: 10.12691/ajma-1-3-1
Copyright © 2013 Science and Education Publishing

Cite this paper:
J.F. Alzaidy. The (G’/G)-Expansion Method and Traveling Wave Solutions for Some Nonlinear PDEs. American Journal of Mathematical Analysis. 2013; 1(3):28-32. doi: 10.12691/ajma-1-3-1.

Correspondence to: J.F. Alzaidy, Mathematics Department, Faculty of Science, Taif University, Kingdom of Saudi Arabia. Email: j-f-h-z @hotmail.com

Abstract

In the present paper, we construct the traveling wave solutions involving parameters of some nonlinear PDEs in mathematical physics via the nonlinear SchrÖdinger (NLS−) equation and the regularized long-wave (RLW) equation by using a simple method which is called the (G’/G) -expansion method, where G=G(ζ) satisfies the second order linear ordinary differential equation. When the parameters are taken special values, the solitary waves are derived from the traveling waves. The traveling wave solutions are expressed by hyperbolic, trigonometric and rational functions. This method is more powerful and will be used in further works to establish more entirely new solutions for other kinds of nonlinear PDEs arising in mathematical physics.

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