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Turkish Journal of Analysis and Number Theory

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

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

**Frequency:**
bimonthly

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

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

### Article

**On Irresolute Topological Vector Spaces-II**

^{1}Mathematics COMSATS Institute of Information Technology, Park Road, Chak Shahzad, 45550 Islamabad, PAKISTAN

^{2}Mathematics, G.C. University, Lahore, Pakistan

*Turkish Journal of Analysis and Number Theory*. 2016, 4(2), 35-38

doi: 10.12691/tjant-4-2-2

Copyright © 2016 Science and Education Publishing

**Cite this paper:**

Muhammad Asad Iqbal, Muhammad Maroof Gohar, Moiz ud Din Khan. On Irresolute Topological Vector Spaces-II.

*Turkish Journal of Analysis and Number Theory*. 2016; 4(2):35-38. doi: 10.12691/tjant-4-2-2.

Correspondence to: Moiz ud Din Khan, Mathematics COMSATS Institute of Information Technology, Park Road, Chak Shahzad, 45550 Islamabad, PAKISTAN. Email: moiz@comsats.edu.pk

### Abstract

### Keywords

### References

[1] | Moiz ud Din Khan, Muhammad Asad Iqbal, On Irresolute topological vector space, Adv. Pure Math. 6(2016), 105-112. | ||

[2] | Muhammad Saddique Bosan, s-Topological groups, 2015, (Ph.D Thesis). | ||

[3] | N. Levine, Semi-Open Sets and Semi-Continuity in Topological Spaces, Amer. math. month., 70(1) (1963), 37-41. | ||

[4] | Crossley, S.G. and Hildebrand, S.K. Semi-Topological Properties. Fundamental Mathematicae, 74(1972), 233-254. | ||

[5] | Crossley, S.G. and Hildebrand, S.K. Semi-Closure, Texas J. Sci., 22(1971), 99-112. | ||

### Article

**Weak Compatibility and Related Fixed Point Theorem for Six Maps in Multiplicative Metric Space**

^{1}Department of Mathematics, Pt. JLN Govt. College Faridabad, Sunrise University, Alwar (Rajasthan), India

^{2}Department of Mathematics, Manav Rachna International University, Faridabad, Haryana, India

^{3}Department of Mathematics, Teerthankar Mahaveer University, Moradabad (U.P), India

^{4}Departtment of Mathematics, Lovely Professional University, Punjab, India

*Turkish Journal of Analysis and Number Theory*. 2016, 4(2), 39-43

doi: 10.12691/tjant-4-2-3

Copyright © 2016 Science and Education Publishing

**Cite this paper:**

Kamal Kumar, Nisha Sharma, Rajeev Jha, Arti Mishra, Manoj Kumar. Weak Compatibility and Related Fixed Point Theorem for Six Maps in Multiplicative Metric Space.

*Turkish Journal of Analysis and Number Theory*. 2016; 4(2):39-43. doi: 10.12691/tjant-4-2-3.

Correspondence to: Manoj Kumar, Departtment of Mathematics, Lovely Professional University, Punjab, India. Email: manojantil18@gmail.com

### Abstract

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### References

[1] | A. Azam, B. Fisher and M. Khan: Common fixed point theorems in Complex valued metric spaces. Numerical Functional Analysis and Optimization. 32(3): 243-253(2011). | ||

[2] | A. E. Bashirov, E. M. Kurplnara and A. Ozyapici, Multiplicative calculus and its applications, J. Math. Anal. Appl., 337 (2008). | ||

[3] | Al Pervo: On the Cauchy problem for a system of ordinary differential equations. Pvi-blizhen met Reshen Diff Uvavn. Vol. 2, pp. 115-134, 1964. | ||

[4] | C. Semple, M. Steel: Phylogenetics, Oxford Lecture Ser. In Math Appl, vol. 24, Oxford Univ. Press, Oxford, 2003. | ||

[5] | Dr. Yogita R. Sharma,Common Fixed Point Theorem in Complex Valued Metric Spaces ISSN: 2319-8753 International Journal of Innovative Research in Science, Engineering and Technology (An ISO 3297: 2007 Certified Organization) Vol. 2, Issue 12, December 2013 | ||

[6] | G. Junck,Commuting maps and fixed points. Am Math Monthly. vol. 83, pp. 261-263,1976. | ||

[7] | L.G. Huang, X. Zhang: Cone metric spaces and fixed point theorem for contractive mappings. J Math Anal Appl. Vol. 332, pp. 1468-1476, 2007. | ||

[8] | MuttalipÖzavsar and adem C. ceviket, fixed points of multiplicative contraction mapping on multiplivate metric spaces arXiv:1205.5131v1 [math.GM]. | ||

[9] | R.P.Agarwal, M. A. El-Gebeily and D. O’Regan, Generalized contractions in partially ordered metric spaces, Applicable Analysis. 87(2008), 109-116. | ||

[10] | R. H. Haghi, Sh. Rezapour and N. Shahzadb; Some fixed point generalizations are not real generalization. Nonlinear Anal.Vol. 74, pp. 1799- 1803, 2011. | ||

[11] | R. Tiwari, D. P. Shukla: Six maps with a common fixed point in complex valued metric spaces. Research J of Pure Algebra. Vol. 2issue 12 pp.365-369, 2012. ISSN: 2319-8753 International Journal of Innovative Research in Science, Engineering and Technology (An ISO 3297: 2007 Certified Organization) Vol. 2, Issue 12, December 2013. | ||

[12] | S. A. Mohiuddine, M. Cancan and H. Sevli, Intuitionistic fuzzy stability of a Jensen functional equation via fixed point technique, Math. Comput.Model. 54 (2011), 2403-2409. | ||

[13] | S. Sessa, On a weak commutativity condition of mappings in fixed point consideration. PublInst Math, 32(46): 149-153(1982). | ||

[14] | S.B.Nadler, Multivalued nonlinear contraction mappings, Pacific J.Math. 30(1969) 475-488. | ||

[15] | Soon-Mo Jung, A Fixed Point Approach to the Stability of Differential Equations y ′ = F(x, y), Bull of the Malys. Math.Sci. Soc. (33) (2010), 47-56. | ||

[16] | T.Suzuki, Subrahmanyam’s fixed point theorem, Nonlinear Analysis, 71(2009) 1678-1683. | ||

[17] | W. Chistyakov, Modular metric spaces, I: basic concepts. Nonlinear Anal. Vol. 72, pp. 1-14, 2010. | ||

[18] | W.Takahashi, Nonlinear Functional Analysis:Fixed point theory and its applications, Yokohama Publishers, 2000. | ||

[19] | Y. Kimura and W. Takahashi, Weak convergence to common fixed points of countable nonexpansive mappings and its applications, Journal of the Korean Mathematical Society 38 (2001), 1275-1284. | ||

### Article

**On the Generalization of Simpson Type Inequalities for Quasi-convex Functions**

^{1}Department of Mathematics, Ordu University, Faculty of Science and Letters, Ordu, Turkey

^{2}Department of Elementary Education, Faculty of Education, Uludağ University, Bursa, Turkey

^{3}Department of Mathematics, Ağrı İbrahim Çeçen University, Faculty of Science and Letters, 04100, Ağrı, Turkey

*Turkish Journal of Analysis and Number Theory*. 2016, 4(2), 44-47

doi: 10.12691/tjant-4-2-4

Copyright © 2016 Science and Education Publishing

**Cite this paper:**

Erhan Set, M. Emin Özdemir, Ahmet Ocak Akdemir. On the Generalization of Simpson Type Inequalities for Quasi-convex Functions.

*Turkish Journal of Analysis and Number Theory*. 2016; 4(2):44-47. doi: 10.12691/tjant-4-2-4.

Correspondence to: Erhan Set, Department of Mathematics, Ordu University, Faculty of Science and Letters, Ordu, Turkey. Email: erhanset@yahoo.com

### Abstract

### Keywords

### References

[1] | M. Alomari, M. Darus and S.S. Dragomir, New inequalities of Simpson’s type for sconvex functions with applications, RGMIA Res. Rep. Coll., 12 (4) (2009), Article 9. [Online: http://www.staff.vu.edu.au/RGMIA/v12n4.asp] | ||

[2] | M. Alomari, M. Darus and S.S. Dragomir, New inequalities of Hermite-Hadamard type for functions whose second derivatives absolute values are quasi-convex, Tamkang J. Math., 41 (4) (2010), 353-359. | ||

[3] | M. Alomari, M. Darus and U.S. Kırmacɪ, Refinements of Hadamard-type inequalities for quasi-convex functions with applications to trapezoidal formula and to special means, Comp. Math. Appl., 59 (2010), 225-232. | ||

[4] | S.S. Dragomir, R.P. Agarwal and P. Cerone, On Simpson’s inequality and applications, J. of Inequal. Appl., 5(2000), 533-579. | ||

[5] | D.A. Ion, Some estimates on the Hermite-Hadamard inequality through quasi-convex functions, Annals of University of Craiova Math. Comp. Sci. Ser., 34 (2007), 82-87. | ||

[6] | Z. Liu, An inequality of Simpson type, Proc. R. Soc. London. Ser A, 461 (2005), 2155-2158. | ||

[7] | M.A. Noor, K.I. Noor, M.U. Awan, Some new Simpson type integral inequalities for differentiable convex functions, preprint (2015). | ||

[8] | J. Pecaric, F. Proschan and Y.L. Tong, Convex functions, partial ordering and statistical applications, Academic Press, New York, 1991. | ||

[9] | E. Set, M.E. Ozdemir, M.Z. Sarıkaya, On new inequalities of Simpson’s type for quasi-convex functions with applications, Tamkang J. Math., 43 (3) (2012), 357-364. | ||