iosr-Jm   Volume-13 ~ Issue-5 ~ Sep-Oct 2017

Abstract: We show that there is a linear functional bounded uniformly on all atoms in . In this work, we first give a new atomic decomposition, where the decomposition converges in rather than only in the distribution sense. Then using this decomposition, we show.........

Keywords: Hardy Spaces, atomic decomposition, quasi-Banach space

[1] M. Bownik, Boundedness of operators on Hardy spaces via atomic decompositions, Proc. Amer. Math. Soc., 133(12) (2005), 3535-3542.
[2] R. R. Coifman, A real variable characterization of Hp, Studia Math., 51 (1974), 269-274.
[3] S. A. Chang and R. Fefferman, The Calder_on-Zygmund decomposition on product domains, Amer. J. Math., 104(3) (1982), 455-468.
[4] R. R. Coifman and G. Weiss, Extensions of Hardy spaces and their use in analysis, Bull. Amer. Math. Soc., 83 (1977), 569-645.
[5] Y. S. Han, Triebel-Lizorkin spaces on spaces of homogeneous type, Studia Math., 108 (1994), 247-273.

Abstract: In this paper, a fixed point theorem for six self-maps has been established using the concept of compatible maps of type ( ), which generalizes the result of Jain et. al. [5]. Mathematics Subject Classification: Primary 47H10, Secondary 54H25.

Keywords:Common fixed points, fuzzy metric space, compatible maps, Weak compatible maps, compatible maps of type ( ).

[1] Cho, S.H., On common fixed point theorems in fuzzy metric spaces, J. Appl. Math. & Computing Vol. 20 (2006), No. 1 -2, 523-533.
[2] Cho, Y.J., Fixed point in Fuzzy metric space, J. Fuzzy Math. 5(1997), 949-962.
[3] George, A. and Veeramani, P., On some results in Fuzzy metric spaces, Fuzzy Sets and Systems 64 (1994), 395-399.
[4] Grabiec, M., Fixed points in Fuzzy metric space, Fuzzy sets and systems, 27(1998), 385-389.
[5] Jain, A., Gupta, V.K., Badshah, V.H. and Chandelkar, R.K., Fixed point theorem in Fuzzy metric space using semi-compatible mappings, Advances in Inequalities and Applications, 19 (2014), 1-10.

Abstract: We have investigated Bianchi type V cosmological model with the matter string dust universe with cosmological constant  in general theory of relativity. And have obtained the deterministic solution of Einstein's field equation, further some physical and geometrical properties of the model are also discussed.

Keywords: Bianchi type V, String dust, cosmological constant  , general theory of relativity

[1] K.S. Adhav, A.S Nimkar, Non-Existence of Bianchi Type- V String Cosmological Model with Bulk Viscous fluid in General
Relativity, Rom. Journ. Phys.54(2) ,2007, 207-212, Bucharest.
[2] K.S. Adhav, S.D Katore, Higher Dimensional Bianchi Type-V Universe in Creation Field Cosmology, Natural Science, 2(5),
2010,484-488.
[3] K.S. Adhav, M.V. Dawande, LRS Bianchi Type-V Universe in Creation Field Cosmology,Bulg. J. Phys. 38, 2011,364-370.
[4] Baghel, Prashant singh ; Singh, Jagdish Prasad, Bianchi Type-V universe with bulk viscous matter and time varying gravitational
and cosmological constants, Research in Astronomy and Astrophysics, 12(11), 2012, 1457-1466.
[5] Bali, Swati Singh, Bianchi Type-V Inflationary universe with decaying vacuum energy (^) , Middle-East Journal of Scientific
Research, 15(8), 2013,1087-1091

Abstract: Let G be a connected graph of order n and degree d, the Acharya Polynomial AP(G, ) is defined as.....

Keywords: Acharya index, Acharya Polynomial, Thorn Tree Thorn rod, Thorn cycle.

[1]. F. Buckley and F. Harary, Distance in Graphs, Addison –Wesley, Redwood (1990).
[2]. Abbas Heydari, Ivan Gutman "On the Terminal Wiener index of the thorn graphs",Kragujevac. J. Sci. 32 ,57(2010) .
[3]. K.P.Narayankar,S.B.Lokesh,S.S.Shirol and H.S.Ramane"Terminal Hosoya polynomial of thorn graphs."Scientia Magna, 9, 37-42,
(2013).
[4]. Shailaja S. Shirkol,H. S. Ramane, ShobhaV. Patil, "On Acharya index of Graph ", Annals of Pure and Applied Mathematics. 11,
No. 1,73- 77,2016).
[5]. Shailaja S. Shirkol, ShobhaV. Patil, "On Acharya Polynomial of Graph ", Annuals of Pure and Applied Mathematics.Vo.
11,No.2,117-121(2016).