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Turkish Journal of Analysis and Number Theory

**ISSN (Print):**
2333-1100

**ISSN (Online):**
2333-1232

**Editor-in-Chief:**
Mehmet Acikgoz, Feng Qi, Cenap Özel

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

### Article

**On the Generalized Degenerate Tangent Numbers and Polynomials**

^{1}Department of Mathematics, Hannam University, Daejeon, Korea

*Turkish Journal of Analysis and Number Theory*. 2015, 3(4), 104-107

doi: 10.12691/tjant-3-4-3

Copyright © 2015 Science and Education Publishing

**Cite this paper:**

Cheon Seoung Ryoo. On the Generalized Degenerate Tangent Numbers and Polynomials.

*Turkish Journal of Analysis and Number Theory*. 2015; 3(4):104-107. doi: 10.12691/tjant-3-4-3.

Correspondence to: Cheon Seoung Ryoo, Department of Mathematics, Hannam University, Daejeon, Korea. Email: ryoocs@hnu.kr

### Abstract

### Keywords

### References

[1] | L. Carlitz, Degenerate Stirling, Bernoulli and Eulerian numbers, Utilitas Math. 15(1979), 51-88. | ||

[2] | L. Carlitz, A degenerate Staudt-Clausen theorem, Arch. Math. (Basel) 7(1956), 28-33. | ||

[3] | F. Qi, D. V. Dolgy, T. Kim, C. S. Ryoo, On the partially degenerate Bernoulli polynomials of the first kind, Global Journal of Pure and Applied Mathematics, 11(2015), 2407-2412. | ||

[4] | T. Kim, Barnes' type multiple degenerate Bernoulli and Euler polynomials, Appl. Math. Comput. 258(2015), 556-564. | ||

[5] | H. Ozden, I. N. Cangul, Y. Simsek, Remarks on q-Bernoulli numbers associated with Daehee numbers, Adv. Stud. Contemp. Math. 18(2009), no. 1, 41-48. | ||

[6] | C. S. Ryoo, A Note on the tangent numbers and polynomials, Adv. Studies Theor. Phys., 7(2013), no. 9, 447-454. | ||

[7] | C. S. Ryoo, Generalized tangent numbers and polynomials associated with p-adic integral on p, Applied Mathematical Sciences, 7(2013), no. 99, 4929-4934. | ||

[8] | C. S. Ryoo, Some identities on the (h; q)-tangent polynomials and Bernstein Polynomials, Applied Mathematical Sciences, 8(2014), no. 75, 3747-3753. | ||

[9] | C. S. Ryoo, Notes on degenerate tangent polynomials, to appear in Global Journal of Pure and Applied Mathematics, Volume 11, number 5(2015), pp. 3631-3637. | ||

[10] | P. T. Young, Degenerate Bernoulli polynomials, generalized factorial sums, and their applications, Journal of Number Theorey, 128(2008), 738-758. | ||

### Article

**Generalized s-topological Groups**

^{1}Department of Mathematics, Preston University Kohat (Islamabad), Pakistan

^{2}Department of Mathematics, COMSATS institute of information technology, Chak Shehzad Islamabad, Pakistan

*Turkish Journal of Analysis and Number Theory*. 2015, 3(4), 108-110

doi: 10.12691/tjant-3-4-4

Copyright © 2015 Science and Education Publishing

**Cite this paper:**

Rehman Jehangir, Moizud Din Khan. Generalized s-topological Groups.

*Turkish Journal of Analysis and Number Theory*. 2015; 3(4):108-110. doi: 10.12691/tjant-3-4-4.

Correspondence to: Moizud Din Khan, Department of Mathematics, COMSATS institute of information technology, Chak Shehzad Islamabad, Pakistan. Email: Jehangir_pk@yahoo.com, moiz@comsats.edu.pk

### Abstract

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### References

[1] | E. Bohn, J. Lee, Semi-topological groups, Amer. Math. Monthly 72 (1965), 996.998. | ||

[2] | Á. Császár, Generalized open sets, Acta Math. Hungar., 75 (1997), 65-87. | ||

[3] | Á. Császár, Generalized topology, generalized continuity, Acta Math.Hungar., 96 (2002), 351-357. | ||

[4] | M. Hussain, M. Khan and C. Ozel, On generalized topological groups, Filomat, 2013 27(4):567-575. | ||

[5] | M. Hussain, M. Khan and C. Ozel, More on generalized topological groups, Creative Math. & Inf. 22(2013)(1), 47-51. | ||

[6] | M. Hussain, M. Khan, A, Z, Özcelik, and C. Ozel, Extension closed properties on generalized topological groups, Arab J Math (2014) 3:341-347. | ||

[7] | N. Levine, Semi-open sets and semi-continuity in topological spaces, Amer. Math. Monthly 70 (1963), 36.41.1. | ||

[8] | Michel Coste, Real Algebraic Sets, March 23, 2005. | ||

[9] | J. Cao, R. Drozdowski, Z. Piotrowski, Weak continuity properties of topologized groups, Czech. Math. J., 60 (2010), 133-148. | ||

[10] | C. Silva and R. Silva, On generalized S topological group, International journal of science and research, 6, (2015), 1-4. | ||

### Article

**Further Inequalities Associated with the Classical Gamma Function**

^{1}Department of Mathematics, University for Development Studies, Navrongo Campus, Navrongo UE/R, Ghana

*Turkish Journal of Analysis and Number Theory*. 2015, 3(4), 111-115

doi: 10.12691/tjant-3-4-5

Copyright © 2015 Science and Education Publishing

**Cite this paper:**

Kwara Nantomah. Further Inequalities Associated with the Classical Gamma Function.

*Turkish Journal of Analysis and Number Theory*. 2015; 3(4):111-115. doi: 10.12691/tjant-3-4-5.

Correspondence to: Kwara Nantomah, Department of Mathematics, University for Development Studies, Navrongo Campus, Navrongo UE/R, Ghana. Email: mykwarasoft@yahoo.com, knantomah@uds.edu.gh

### Abstract

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### References

[1] | Y. C. Chen, T. Mansour and Q. Zou, On the complete monotonicity of quotient of Gamma functions, Math. Ineq. & Appl. 15:2 (2012), 395-402. | ||

[2] | R. Diaz and E. Pariguan, On hypergeometric functions and Pachhammer k-symbol, Divulgaciones Matematicas 15(2)(2007), 179-192. | ||

[3] | R. Diaz and C. Teruel, q,k-generalized gamma and beta functions, J. Nonlin. Math. Phys. 12(2005), 118-134. | ||

[4] | T. Mansour, Some inequalities for the q-Gamma Function, J. Ineq. Pure Appl. Math. 9(1)(2008), Art. 18. | ||

[5] | T. Mansour and A.Sh. Shabani, Some inequalities for the q-digamma function, J. Ineq. Pure and Appl. Math. 10:1 (2009), Article 12. | ||

[6] | T. Mansour and A. Sh. Shabani, Generalization of some inequalities for the (q_{1} ….. q_{s})-Gamma function, Le Matematiche LXVII (2012), 119-130. | ||

[7] | F. Merovci, Power Product Inequalities for the Function, Int. Journal of Math. Analysis, 4(21)(2010), 1007-1012. | ||

[8] | V. Krasniqi and F. Merovci, Some Completely Monotonic Properties for the (p,q)-Gamma Function, Mathematica Balkanica, New Series 26(2012), 1-2. | ||

[9] | V. Krasniqi, T. Mansour and A. Sh. Shabani, Some Monotonicity Properties and Inequalities for and Functions, Mathematical Communications 15(2) (2010), 365-376. | ||

[10] | V. Krasniqi, T. Mansour, and A. Sh. Shabani, Some inequalities for q-polygamma function and zeta q-Riemann zeta functions, Ann. Math. Informaticae, 37 (2010), 95-100. | ||

[11] | K. Nantomah and M. M. Iddrisu, Some Inequalities Involving the Ratio of Gamma Functions, Int. Journal of Math. Analysis 8(12)(2014), 555-560. | ||

[12] | K. Nantomah, M. M. Iddrisu and E. Prempeh, Generalization of Some Inequalities for theRatio of Gamma Functions, Int. Journal of Math. Analysis, 8(18)(2014), 895-900. | ||

[13] | K. Nantomah and E. Prempeh, Generalizations of Some Inequalities for the p-Gamma, q-Gamma and k-Gamma Functions, Electron. J. Math. Anal. Appl. 3(1)(2015),158-163. | ||

[14] | K. Nantomah and E. Prempeh, Some Sharp Inequalities for the Ratio of Gamma Functions, Math. Aeterna, 4(5)(2014), 501-507. | ||

[15] | K. Nantomah and E. Prempeh, Generalizations of Some Sharp Inequalities for the Ratio of Gamma Functions, Math. Aeterna, 4(5)(2014), 539-544. | ||

[16] | K. Nantomah, On Certain Inequalities Concerning the Classical Euler's Gamma Function, Advances in Inequalities and Applications, Vol. 2014 (2014) Article ID 42. | ||

[17] | K. Nantomah, Generalized Inequalities Related to the Classical Euler's Gamma Function, Turkish Journal of Analysis and Number Theory, 2(6)(2014), 226-229. | ||

[18] | K. Nantomah, Further Inequalities Associated with the Classical Gamma Function, arXiv:1506.07393v1. | ||