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 Özel

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

Google-based Impact Factor: 2.54   Citations

Article

Some Identities of Tribonacci Polynomials

1School of Studies in Mathematics, Vikram University Ujjain, (M. P.), India

2Department of Mathematical Sciences and Computer applications, Bundelkhand University, Jhansi (U. P.), India


Turkish Journal of Analysis and Number Theory. 2016, 4(1), 20-22
doi: 10.12691/tjant-4-1-4
Copyright © 2016 Science and Education Publishing

Cite this paper:
Yogesh Kumar Gupta, V. H. Badshah, Mamta Singh, Kiran Sisodiya. Some Identities of Tribonacci Polynomials. Turkish Journal of Analysis and Number Theory. 2016; 4(1):20-22. doi: 10.12691/tjant-4-1-4.

Correspondence to: Yogesh  Kumar Gupta, School of Studies in Mathematics, Vikram University Ujjain, (M. P.), India. Email: yogeshgupta.880@rediffmail.com

Abstract

The Tribonacci polynomial is famous for possessing wonderful and amazing properties. Tribonacci polynomials tn(x) defined by the recurrence relation tn+3(x)=x2tn+2(x)+xtn+1(x)+tn(x) for n0 with to(x) =o, t1(x)=1, t2(x)=x2. In this paper, we introduce some identities Tribonacci polynomials by standard techniques.

Keywords

References

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[17]  W.Goh, M.x. He, P.E. Ricci, on the universal zero attrattor of the Tribonacci- Related Polynomials, (2009).
 
[18]  Yogesh Kumar Gupta, V. H. Badshah, Mamta Singh, and Kiran Sisodiya, Generalized Additive Coupled Fibonacci Sequences of Third order and Some Identities, International Journal of Innovative Science, Engineering & Technology, Vol. 2 Issue 3, March 2015, 80-85.
 
[19]  Yogesh Kumar Gupta, Kiran Sisodiya, Mamta Singh, and Generalization of Fibonacci Sequence and Related Properties, “Research Journal of Computation and Mathematics, Vol. 3, No. 2, (2015), 12-18.
 
[20]  Yogesh Kumar Gupta, V. H. Badshah, Mamta Singh, and Kiran Sisodiya, “Diagonal Function of k-Lucas Polynomials.” Turkish Journal of Analysis and Number Theory, vol. 3, no. 2 (2015): 49-52.
 
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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

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[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

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[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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[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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