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 Fixed Point Theorems of Integral Type Contraction in Cone b-metric Spaces

1Department of Mathematics, University of Peshawar, Peshawar, Pakistan


Turkish Journal of Analysis and Number Theory. 2015, 3(6), 165-169
doi: 10.12691/tjant-3-6-5
Copyright © 2015 Science and Education Publishing

Cite this paper:
Rahim Shah, Akbar Zada, Ishfaq Khan. Some Fixed Point Theorems of Integral Type Contraction in Cone b-metric Spaces. Turkish Journal of Analysis and Number Theory. 2015; 3(6):165-169. doi: 10.12691/tjant-3-6-5.

Correspondence to: Rahim  Shah, Department of Mathematics, University of Peshawar, Peshawar, Pakistan. Email: safeer_rahim@yahoo.com

Abstract

In the present paper, we introduces the concept of integral type contraction with respect to cone b-metric space. Also we proved some fixed point results of integral type contractive mapping in cone b-metric space. We give an example to support our main result.

Keywords

References

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[2]  A. Azam, M. Arshad, I. Beg, Banach contraction principle on cone rectengular metric spaces, Applicable Anal. Discrete Math., vol. 3, 2009, pp. 236-241.
 
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[5]  M. Boriceanu, Strict fixed point theorems for multivalued operators in b-metric spaces, Intern. J. Modern Math., vol. 4(3), 2009, pp. 285-301.
 
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[8]  A. Branciari, A _xed point theorem for mappings satisfying a general contractive condition of integral type, International Journal of Mathematics and Mathematical Sciences, vol. 29, no. 9, 2002, pp. 531-536.
 
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Article

Studies on Fractional Differential Operators of Two Parameters in a Complex Domain

1Institute of Mathematical Sciences, University Malaya, 50603, Malaysia

2Faculty of Computer Science and Information Technology, University, Malaya, 50603, Malaysia


Turkish Journal of Analysis and Number Theory. 2016, 4(1), 1-7
doi: 10.12691/tjant-4-1-1
Copyright © 2016 Science and Education Publishing

Cite this paper:
Rabha W. Ibrahim, Hamid A. Jalab. Studies on Fractional Differential Operators of Two Parameters in a Complex Domain. Turkish Journal of Analysis and Number Theory. 2016; 4(1):1-7. doi: 10.12691/tjant-4-1-1.

Correspondence to: Rabha  W. Ibrahim, Institute of Mathematical Sciences, University Malaya, 50603, Malaysia. Email: rabhaibrahim@yahoo.com

Abstract

This study deals with a generalization for fractional differential operators in a complex domain based on the extended Beta function. Stipulations are imposed for these generalized operators such as the upper bounds. Other possessions for the above operator are also prepared. In addition, implementations of these operators are introduced and suggested in the geometric function theory (GFT). Sufficient conditions are imposed for functions to be univalent.

Keywords

References

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[4]  Ibrahim RW, On generalized Srivastava-Owa fractional operators in the unit disk, Advances in Difference Equations 2011, 2011:55.
 
[5]  Srivastava HM, Agarwal P, Jain S, Generating functions for the generalized Gauss hypergeometric functions, Appl. Math. Comput. 247, 2014: 348-352.
 
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[8]  Ӧzergin E, Ӧzarslan MA, Altin A: Extension of gamma, beta and hypergeometric functions, J. Comput. Appl. Math. 235, 2011: 4601-4610.
 
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[10]  Tremblay R, Une contribution a la theori de la derivee fractionnaire [Ph.D. thesis ]. Quebec. Canada: Laval University; 1974.
 
[11]  Ibrahim RW, Jahangiri M, Boundary fractional differential equation in a complex domain, Boundary Value Problems 2014, 2014:66.
 
[12]  Ibrahim RW, et al., Third-order differential subordination and superordination involving a fractional operator, Open Math. 13, 2015: 706-728.
 
[13]  Ibrahim RW, et al., Upper and lower bounds of integral operator defined by the fractional hypergeometric function, Open Math. 13, 2015: 768-780.
 
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Article

On the Bounds of the First Reformulated Zagreb Index

1Department of Mathematics, University of Haifa, 3498838 Haifa, Israel

2Institute for Computer Science, Friedrich Schiller University Jena, Germany

3Department of Mathematics, Velammal Engineering College, Surapet, Chennai-66, Tamil Nadu, India

4Department of Mathematics, Sacred Heart College, Tirupattur-635601, Tamil Nadu, India


Turkish Journal of Analysis and Number Theory. 2016, 4(1), 8-15
doi: 10.12691/tjant-4-1-2
Copyright © 2016 Science and Education Publishing

Cite this paper:
T. Mansour, M. A. Rostami, E. Suresh, G. B. A. Xavier. On the Bounds of the First Reformulated Zagreb Index. Turkish Journal of Analysis and Number Theory. 2016; 4(1):8-15. doi: 10.12691/tjant-4-1-2.

Correspondence to: E.  Suresh, Department of Mathematics, Velammal Engineering College, Surapet, Chennai-66, Tamil Nadu, India. Email: sureshkako@gmail.com

Abstract

The edge version of traditional first Zagreb index is known as first reformulated Zagreb index. In this paper, we analyze and compare various lower and upper bounds for the first reformulated Zagreb index and we propose new lower and upper bounds which are stronger than the existing and recent results [Appl. Math. Comp. 273 (2016) 16-20]. In addition, we prove that our bounds are superior in comparison with the other existing bounds.

Keywords

References

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[5]  K. C. Das, K. Xu and J. Nam, Zagreb indices of graphs, Front. Math. China 10 (2015) 567-582.
 
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