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

Fractional Integral Inequalities via s-Convex Functions

1Atatürk University, K.K. Education Faculty, Department of Mathematics, 25240, Campus, Erzurum, Turkey

2Uludağ University, Education Faculty, Department of Mathematics, 16059, Bursa, Turkey

3Van Yüzüncü Yil University, Faculty of Education, Department of Mathematics Education, Van, Turkey


Turkish Journal of Analysis and Number Theory. 2017, 5(1), 18-22
doi: 10.12691/tjant-5-1-4
Copyright © 2017 Science and Education Publishing

Cite this paper:
Çetin Yildiz, M. Emіn Özdemіr, Havva Kavurmaci Önalan. Fractional Integral Inequalities via s-Convex Functions. Turkish Journal of Analysis and Number Theory. 2017; 5(1):18-22. doi: 10.12691/tjant-5-1-4.

Correspondence to: Çetin  Yildiz, Atatürk University, K.K. Education Faculty, Department of Mathematics, 25240, Campus, Erzurum, Turkey. Email: cetin@atauni.edu.tr

Abstract

In this paper, we establish several inequalities for s-convex mappings that are connected with the Riemann-Liouville fractional integrals. Our results have some relationships with certain integral inequalities in the literature.

Keywords

References

[1]  S.S. Dragomir and R.P. Agarwal. Two inequalities for differentiable mappings and applications to special means of real numbers and to trapezoidal formula, Appl. Math. Lett., 11(5)(1998), 91-95.
 
[2]  H. Hudzik and L. Maligranda. Some remarks on s-convex functions, Aequationes Math., 48 (1994), 100-111.
 
[3]  W. Orlicz. A note on modular spaces-I, Bull. Acad. Polon. Sci. Math. Astronom. Phys., 9 (1961), 157-162.
 
[4]  W. Matuszewska and W. Orlicz. A note on the theory of s-normed spaces of φ-integrable functions, Studia Math., 21 (1981), 107-115.
 
[5]  J. Musielak. Orlicz spaces and modular spaces, Lecture Notes in Mathematics, Vol. 1034, Springer-Verlag, New York / Berlin, 1983.
 
Show More References
[6]  S.S. Dragomir and S. Fitzpatrick. The Hadamard.s inequality for s-convex functions in the second sense, Demonstratio Math., 32 (4) (1999), 687-696.
 
[7]  U.S. Kırmacı, M.K. Bakula, M.E. Özdemir and J. Pečarić. Hadamard-type inequalities for s-convex functions, Appl. Math. Comput., 193 (2007), 26-35.
 
[8]  S.S. Dragomir, C.E.M. Pearce. Selected topics on Hermite-Hadamard inequalities and applications, RGMIA monographs, Victoria University, 2000. [Online: http://www.staff.vu.edu.au/RGMIA/monographs/hermite-hadamard.html].
 
[9]  S.G. Samko, A.A Kilbas and O.I. Marichev. Fractional Integrals and Derivatives Theory and Application, Gordan and Breach Science, New York, 1993.
 
[10]  M.Z. Sarikaya, E. Set, H. Yaldız and N. Başak. Hermite-Hadamards inequalities for fractional integrals and related fractional inequalities, Math. Comput. Model., 57 (9-10) (2013), 2403-2407.
 
[11]  M.Z. Sarikaya and H. Ogunmez. On new inequalities via Riemann-Liouville fractional integration, Abst. Appl. Anal., 2012.
 
[12]  E. Set, M.Z. Sarikaya, M.E. Özdemir and H. Yıldırım. The Hadamards inequality for some convex functions via fractional integrals and related results, Jour. of Appl. Math., Statis. Infor., 10 (2) (2014), 69-83.
 
[13]  S. Belarbi and Z. Dahmani. On some new fractional integral inequalities, J. Ineq. Pure and Appl. Math., 10(3) (2009), Art. 86.
 
[14]  Z. Dahmani. New inequalities in fractional integrals, International Journal of Nonlinear Science, 9(4) (2010), 493-497.
 
[15]  Z. Dahmani, On Minkowski and Hermite-Hadamard integral inequalities via fractional integration, Ann. Funct. Anal. 1(1) (2010), 51-58.
 
[16]  Z. Dahmani, L. Tabharit, S. Taf. Some fractional integral inequalities, Nonl. Sci. Lett. A., 1(2) (2010), 155-160.
 
[17]  Z. Dahmani, L. Tabharit, S. Taf. New generalizations of Grüss inequality using Riemann-Liouville fractional integrals, Bull. Math. Anal. Appl., 2(3) (2010), 93-99.
 
[18]  M.E. Özdemir, S.S. Dragomir and Ç. Yıldız. The Hadamard’s inequality for convex function via fractional integrals, Acta Math. Sci., 2013, 33B (5), 1293-1299.
 
Show Less References

Article

First Zagreb Index, F-index and F-coindex of the Line Subdivision Graphs

1Department of Mathematics, Islamic Azad University, Qaemshahr Branch, Qaemshahr, Iran

2Department of Mathematics, Allame Tabarsi Institute, Qaemshahr, Iran


Turkish Journal of Analysis and Number Theory. 2017, 5(1), 23-26
doi: 10.12691/tjant-5-1-5
Copyright © 2017 Science and Education Publishing

Cite this paper:
S. Ghobadi, M. Ghorbaninejad. First Zagreb Index, F-index and F-coindex of the Line Subdivision Graphs. Turkish Journal of Analysis and Number Theory. 2017; 5(1):23-26. doi: 10.12691/tjant-5-1-5.

Correspondence to: S.  Ghobadi, Department of Mathematics, Islamic Azad University, Qaemshahr Branch, Qaemshahr, Iran. Email: Ghobadimath46@gmail.com

Abstract

In this paper we investigate first Zagreb index, F-index and F-coindex of the line graph of some chemical graphs using the subdivision concept.

Keywords

References

[1]  Baskar Babujee, J. and Ramakrishnan, S. “Zagreb indices and coindices for compound graphs,” in: R. Nadarajan, R. S. Lekshmi, G. Sai Sundara Krishnan (Eds.), Computational and Mathematical Modeling, Narosa, New Delhi, pp. 357-362. (2012).
 
[2]  Beineke, L.W.. “Characterizations of derived graphs,” Journal of combinatorial theory, 9. 129-135. (1970).
 
[3]  Chartrand, G. and Zhang, P.. Introduction to graph theory, Mcgraw-Hill, Kalamazoo, MI, (2004).
 
[4]  K. C. Das, K. C., Gutman, I. and Horoldagva, B.. “Comparing Zagreb indices and coindices of trees,” MATCH Commun. Math. Comput. Chem. 68. 189-198. (2012).
 
[5]  De, N., Abu Nayeem, Sk.Md. and Anita Pal. “The F-index of some graph operations,” springer plus 5:221. (2016).
 
Show More References
[6]  Doslić, T.. “Vertex-weighted Wiener polynomials for composite graphs,” Ars Math.Contemp. 1. 66-80. (2008).
 
[7]  Furtula, B. and Gutman, I.. “A forgotten topological index,” J. Math. Chem. 53. 1184-1190. (2015).
 
[8]  Gutman, I., Trinajstić, N.. “Graph theory and molecular orbitals, total π-electron energy of alternant hydrocarbons,” Chem. Phys. Lett. 17. 535-538. (1972).
 
[9]  Hossein Zadeh, S., Hamzeh, A. and Ashrafi, A. R.” Extermal properties of Zagreb coindices and degree distance of graphs,” Miskolc Math. Notes 11. 129-138.( 2010).
 
[10]  Hua, H. and Zhang, S. “Relations between Zagreb coindices and some distance-based topological indices,” MATCH Commun. Math. Comput. Chem. 68. 199-208. (2012).
 
[11]  Kovijanić Vukičević, Z. and Popivoda, G. “Chemical trees with extreme values of Zagreb indices and coindices,” Iran. J. Math. Chem. 5(1). 19-29. (2014).
 
[12]  Nadeem, M.F., Zafar, S. and Zahid, Z. “On certain topological indices of the line graph of subdivision graphs,” Appl. Math. Comput. (2015).
 
[13]  Nikolić, S., Kovačević, G., Miličević, A. and Trinajstić, N. “The Zagreb indices 30 years after,” Croat. Chem. Acta 76. 113-124. (2003).
 
[14]  Ranjini, P.S., Lokesha, V. and Cangl, I.N.. “On the Zagreb indices of the line graphs of the subdivision graphs,” Appl. Math. Comput. 218. 699–702. (2011).
 
[15]  Ranjini, P.S., Lokesha, V. and Rajan, M.A.. “On the Shultz index of the subdivision graphs,” Adv. Stud. Contemp. Math. 21(3). 79-290. (2011).
 
[16]  Shirai, T.. “Spectrum of Infinite Regular Line Graphs” Transactions of the American Mathematical Society. 352, Number 1. 115-132. (1999).
 
[17]  Su, G. and Xu, L.. “Topological indices of the line graph of subdivision graphs and their Schur-bounds,” Appl. Math. Comput. 253. 395-401. (2015).
 
[18]  Wang, M. and Hua, H. “More on Zagreb coindices of composite graphs,” Int. Math. Forum 7. 669-673. (2012).
 
[19]  Whintney, H.. “Congruent Graphs and the connectivity of graphs,” American Journal of Mathematics. 54, 150-168. (1932).
 
Show Less References

Article

Conformal Curvature Tensor on Para-kenmotsu Manifold

1Department of Mathematics, Vignan Institute of Information Technology, Visakhapatnam, Andhra Pradesh, India

2Department of Mathematics, Gayatri Vidya Parishad College of Engineering for Women, Visakhapatnam, Andhra Pradesh, India

3Department of Mathematics, Jawaharlal Nehru Technological University, Kakinada, Andhra Pradesh, India


Turkish Journal of Analysis and Number Theory. 2017, 5(2), 27-30
doi: 10.12691/tjant-5-2-1
Copyright © 2017 Science and Education Publishing

Cite this paper:
S.Sunitha Devi, K.L.Sai Prasad, G.V.S.R. Deekshitulu. Conformal Curvature Tensor on Para-kenmotsu Manifold. Turkish Journal of Analysis and Number Theory. 2017; 5(2):27-30. doi: 10.12691/tjant-5-2-1.

Correspondence to: K.L.Sai  Prasad, Department of Mathematics, Gayatri Vidya Parishad College of Engineering for Women, Visakhapatnam, Andhra Pradesh, India. Email: klsprasad@yahoo.com

Abstract

The object of this paper is to obtain the characterisation of para-Kenmotsu (briefly P-Kenmotsu) manifold satisfying the conditions R,X).C-C,X).R= 0 and R,X).C-C,X).R=LcQ(g,C), where C(X,Y) is the Weyl-conformal curvature tensor, Lc is some function and X∈ T(Mn). It is shown respectively that the P-Kenmotsu manifold with these conditions is an η-Einstein manifold and the manifold is either conformally flat (or) Lc = -1 holds on the manifold.

Keywords

References

[1]  Adati, T. and Matsumoto, K, On conformally recurrent and conformally symmetric P-Sasakian manifolds, TRU Math., 13, 25-32, 1977.
 
[2]  Adati, T. and Miyazawa, T, On P-Sasakian manifolds satisfying certain conditions, Tensor (N.S.), 33, 173-178, 1979.
 
[3]  Ahmet Yildiz, Mine Turan and Bilal Eftal Acet, On para Sasakian manifolds, Dumlupinar Universitesi Fen Bilimleri Enstitusu Dergisi, 24, 27-34, 2011.
 
[4]  Bishop, R. L. and Goldberg, S. I, On conformally flat spaces with commuting curvature and Ricci transformations, Canad. J. Math., 14(5), 799-804, 1972.
 
[5]  Chaki, M. C. and Gupta, B, On conformally symmetric spaces, Indian J. Math., 5, 113-122, 1963.
 
Show More References
[6]  Cihan Ozgur, On a class of Para-Sasakian Manifolds, Turk J. Math., 29, 249-257, 2005.
 
[7]  De, U. C. and Tarafdar, D, On a type of P-Sasakian manifold, Math. Balkanica (N.S.), 7, 211-215, 1993.
 
[8]  Deszcz, R, On pseudosymmetric spaces, Bull. Soc. Math. Belg., 49, 134-145, 1990.
 
[9]  Kenmotsu, K, A class of almost contact Riemannian manifolds, Tohoku Math. Journal, 24, 93-103, 1972.
 
[10]  Sato, I, On a structure similar to the almost contact structure, Tensor (N.S.), 30 , 219-224, 1976.
 
[11]  Sato, I. and Matsumoto, K, On P-Sasakian satisfying certain conditions, Tensor (N.S.), 33, 173-178, 1979.
 
[12]  Satyanarayana, T. and Sai Prasad, K. L, On a type of Para Kenmotsu Manifold, Pure Mathematical Sciences, 2(4), 165-170, 2013.
 
[13]  Sinha, B. B. and Sai Prasad, K. L, A class of almost para contact metric Manifold, Bulletin of the Calcutta Mathematical Society, 87, 307-312, 1995.
 
Show Less References