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

Google-based Impact Factor: 2.54   Citations

Article

On Irresolute Topological Vector Spaces-II

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

2Mathematics, 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

In this paper, we continue the study of Irresolute topological vector spaces. Notions of convex, bounded and balanced set are introduced and studied for Irresolute topological vector spaces. Along with other results, it is proved that: 1. Irresolute topological vector spaces are semi-Hausdorff spaces. 2. Every Irresolute topological vector space is semi-regular space. 3. In Irresolute topological vector spaces, as well as is convex if is convex. 4. In Irresolute topological vector spaces, is bouned if is bounded. 5. In Irresolute topological vector spaces, is balanced if is balanced and 6. In Irresolute topological vector spaces, every semi compact set is bounded.

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

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

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

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

4Departtment 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

We consider six self-maps satisfying the condition of commuting and weak compatibility of mappings and the purpose of this paper is to give some common fixed points theorems for complete multiplicative metric space.

Keywords

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
 
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[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].
 
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[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.
 
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[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.
 
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Article

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

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

2Department of Elementary Education, Faculty of Education, Uludağ University, Bursa, Turkey

3Department 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

In this paper, we establish the generalization of inequalities of the Simpson type for functions whose absolute values of derivatives are quasi-convex.

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.
 
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[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.
 
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