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

An Extended Coupled Coincidence Point Theorem

1Republic of Turkey Ministry of National Education, Mathematics Teacher, 60000 Tokat, Turkey

2Department of Civil Engineering, Faculty of Engineering, Şırnak University, 73000, Turkey

3Department of Mathematics, Faculty of Science, Ataturk University, Erzurum, 25240, Turkey


Turkish Journal of Analysis and Number Theory. 2016, 4(1), 23-30
doi: 10.12691/tjant-4-1-5
Copyright © 2016 Science and Education Publishing

Cite this paper:
Esra Yolacan, Mehmet Kir, Hukmi Kiziltunc. An Extended Coupled Coincidence Point Theorem. Turkish Journal of Analysis and Number Theory. 2016; 4(1):23-30. doi: 10.12691/tjant-4-1-5.

Correspondence to: Mehmet  Kir, Department of Civil Engineering, Faculty of Engineering, Şırnak University, 73000, Turkey. Email: mehmetkir@sirnak.edu.tr

Abstract

In this paper, we prove some coupled coincidence point theorem for a pair {F,G} of mappings F,G:C2→C without mixed G-monotone property of F. Our results improve and generalize results given by Karapinar et al. (Arab J Math (2012) 1: 329-339) and Jachymski (Nonlinear Anal. 74, 768-774 (2011)). The theoretic results are also accompanied with suitable example.

Keywords

References

[1]  Bhaskar, TG, Lakshmikantham, V: Fixed point theorems in partially ordered metric spaces and applications. Nonlinear Anal. 65, 1379-1393 (2006).
 
[2]  Lakshmikantham, V, Ćirić, LB: Coupled .xed point theorems for nonlinear contractions in partially ordered metric spaces. Nonlinear Anal. 70, 4341-4349 (2009).
 
[3]  Hussain et al.: Coupled coincidence point results for a generalized compatible pair with applications. Fixed Point Theory and Applications 2014, 2014: 62.
 
[4]  Choudhury, B, Kundu, A: A coupled coincidence point result in partially ordered metric spaces for compatible mappings. Nonlinear Anal. 73, 2524-2531 (2010).
 
[5]  Karapinar, E, Luong, NV, Thuan, NX: Coupled coincidence point for mixed monotone operators in partially ordered metric spaces. Arab J Math (2012) 1: 329-339.
 
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[6]  Jachymski, J: Equivalent conditions for generalized contractions on (ordered) metric spaces. Nonlinear Anal. 74, 768-774 (2011).
 
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Article

On Fixed Points for Chatterjea’s Maps in b-Metric Spaces

1Department of Mathematics and Physics, University of Food Technologies, Plovdiv, Bulgaria

2Faculty of Mathematics and Informatics, Plovdiv University “Paisii Hilendarski”, Plovdiv, Bulgaria


Turkish Journal of Analysis and Number Theory. 2016, 4(2), 31-34
doi: 10.12691/tjant-4-2-1
Copyright © 2016 Science and Education Publishing

Cite this paper:
Radka Koleva, Boyan Zlatanov. On Fixed Points for Chatterjea’s Maps in b-Metric Spaces. Turkish Journal of Analysis and Number Theory. 2016; 4(2):31-34. doi: 10.12691/tjant-4-2-1.

Correspondence to: Radka  Koleva, Department of Mathematics and Physics, University of Food Technologies, Plovdiv, Bulgaria. Email: r.p.koleva@gmail.com

Abstract

In this paper we find sufficient conditions for the existence and uniqueness of fixed points of Chatterjea’s maps in b-metric space. These conditions do not involve the b-metric constant. We establish a priori error estimate for the sequence of successive iterations. The error estimate, which we present is better that the well-known one for a wide class of Chatterjea’s maps in metric spaces.

Keywords

References

[1]  Allahyari, R., Arab, R., Haghighi A.S., “A generalization on weak contractions in partially ordered b-metric spaces and its application to quadratic integral equations”, Journal of Inequalities and Applications, 2014 (355), 2014.
 
[2]  Bakhtin, I.A., “The contraction mapping principle in almost metric spaces”, Funct. Anal., Gos. Ped. Inst., Unianowsk, 30, 26-37, 1989.
 
[3]  Banach, S., “Sur les opérations dans les ensembles abstraits et leur application aux équations integrals”, Fund. Math., 3, 133-181, 1922.
 
[4]  Berinde, V., Iterative approximation on fixed points, Springer, Berlin, 2007.
 
[5]  Bota, M., Molnár, A., Varga, C., “On Ekeland’s variationals principle in b-metric spaces”, Fixed point theory, 12 (2), 21-28, 2011.
 
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[6]  Chatterjea, S., “Fixed point theorems”, C. R. Acad. Bulgare Sci. 25, 727-730, 1972.
 
[7]  Czrezvik, S., “Contraction mappings in b-metric spaces”, Acta Mathematica et Informatica Universitatis Ostravlensis, 1 (1), 5-11, 1993.
 
[8]  Dubey, A.K., Shukla, R., Dubey, R.P., “Some fixed point results in b-metric spaces”, Asian journal of mathematics and applications, 2014, Article ID ama0147, 6 pages, 2014.
 
[9]  George, R., Fisher, B., “Some generalized results of fixed points in cone b-metric spaces”, Mathematica Moravica, 17 (2), 39-50, 2013.
 
[10]  Farkas, C., Molnár, A.E., Nagy, S., “A generalized variational principle in b-metric spaces”, Le Matematiche, LXIX, 205-221, 2014.
 
[11]  Isufati, A., “Rational Contractions in b-Metric Spaces”, Journal of Advances in Mathematics, 5 (3), 803-811, Jan, 2014.
 
[12]  Mehmet K., Hükmi K., “On Some Well Known Fixed Point Theorems in b-Metric Spaces”, Turkish Journal of Analysis and Number Theory, 1 (1), 13-16, 2013.
 
[13]  Mishra, P.K., Sachdeva, S., Banerjee, S.K., “Some fixed point theorems in b-metric space”,Turkish Journal of Analysus and Number Theory, 2 (1), 19-22, 2014.
 
[14]  Rhoades, B.E., “A comparison of various definitions of contractive mappings”, Transactions of the American Mathematical Society, 226, 257-290, 1977.
 
[15]  Rhoades, B.E., Sessa, S., Khan, M.S., Khan, M.D., “Some fixed point theorems for Hardy-Rogers type mappings, Internat. J. Math. & Math. Sci., 7(1), 75-87, 1984.
 
[16]  Sintunavarat, W., Plubtieng, S., Katchang, P., “Fixed point result and applications on b-metric space endowed with an arbitrary binary relation”, Fixed Point Theory Appl., Article ID 296, 2013.
 
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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.