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1
TitleQuadruple Fixed Point Theorems for Multivalued Mappings Under ??−?? Contraction on Partially Ordered Metric Spaces
Vol.38(6) (2014) page: 771-790
Author(s): B. Deshpande and A. Handa  
Abstract:

In this paper, we introduce the concept of w−compatibility and weakly commutativity for the hybrid pair of mappings F:X4→ 2X and g:X→ X and establish a quadruple fixed point theorem for multivalued mapping under φ−ψ contraction in the context of partially ordered metric spaces. As an application of the first theorem, we obtain a quadruple coincidence and common quadruple fixed point for hybrid pair of mappings. We also give examples to illustrate our results. We also improve and generalize several known results.


Keywords: Metric space; Quadruple fixed point; Quadruple coincidence point; ??−?? contraction.
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2
TitleInitial Boundary Value Problems for a Class of N- Dimensional Nonlinear Wave Systems of Fourth Order
Vol.38(6) (2014) page: 791-802
Author(s): L.J. Ding and L.M. Xiao  
Abstract:

In this paper, we study the initial boundary value problem for a class of n-dimensional nonlinear wave systems of fourth order, the existence and the uniqueness of global strong solution to the problem are proved by means of the Galerkin method.


Keywords: Nonlinear wave systems; Initial boundary value problem; Global strong solution.
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3
TitleOn Some Superficial Sequences
Vol.38(6) (2014) page: 803-811
Author(s): L.V. Dinh, N.T. Manh and T.T.H. Thanh  
Abstract:

The paper proves that the superficial sequences in [13, 15, 16, 25] are the weak-(FC)-sequences in [18]. This follows that [18, Theorem 3.4] of Viet in 2000 covers the results of Risler and Teissier [13] in 1973; Trung [15, Theorem 3.4] in 2001; Trung and Verma [16, Theorem 1.4] in 2007. The paper unified the results for mixed multiplicities of ideals in [13, 15, 16, 17, 18, 25].


Keywords: Noetherian ring; Mixed multiplicity; Superficial sequence; Weak-(FC)-sequence.
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4
TitleResults on Meromorphic Functions Having Maximal Deficiency Sum
Vol.38(6) (2014) page: 813-823
Author(s): X.M. Li, X. Zhang and H.X. Yi  
Abstract:

We prove that if f is a transcendental meromorphic function of finite hyper-order such that ∑a ∈ \BbbC∪{∞}δ(a,f)=2, then f is of regular growth and

K(f(k))=\tfrac2k(1−δ(∞,f))1+k−kδ(∞,f),

where

K(f(k))=
lim
r→∞ 
\tfracN(r,1/f(k))+N(r,f(k))T(r,f(k)).

This result improves Theorem 1 [3] and the corresponding result in Singh and Kulkarni [8]. Moreover, by proving the main result of this paper, we will correct the a defective reasoning in the proof of Theorem 1.3 [9], which was resulted from an incorrect result of Lemma 8 [9]. An example is also provided to show that the conclusion of Lemma 8 [9] is incorrect.


Keywords: Meromorphic function; Nevanlinna's deficency; Finite hyper-order; Maximal deficiency sum.
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5
TitleInteraction of Waves Involving Delta-Shocks in the Chaplygin Gas Equations
Vol.38(6) (2014) page: 825-846
Author(s): J.J. Liu, T. Zhou and H.C. Yang  
Abstract:

This paper solves constructively the Riemann problem of the Chaplygin gas equations with three constant states as its initial data. Under suitable generalized Rankine-Hugoniot relations and entropy conditions, the interaction of waves is studied, thirteen kinds of different structures of solutions involving delta-shocks are obtained. Some numerical simulations completely coinciding with the theoretical analysis are also exhibited.


Keywords: Chaplygin gas equations; Delta shock wave; Contact discontinuity; Interaction of waves; Numerical simulations.
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6
TitleArc-Transitive Abelian Cayley Graphs of Certain Valencies
Vol.38(6) (2014) page: 847-855
Author(s): J. Ma  
Abstract:

In this paper, by constructing the abelian covering graphs of bouquet graphs, all the arc-transitive 5-valent abelian Cayley graphs are classified. One new arc-transitive abelian Cayley graph on abelian group \mathbb Z4 2 is given which does not appear in the classification of Alaeiyan et al. [M. Alaeiyan, A. A. Talebi and K. Paryab, Arc-Transitive Cayley Graphs of Valency Five on Abelian Groups, Southeast Asian Bull. Math. 32 (2008), 1029-1035]. Moreover, some of the results are generized to higher valency.


Keywords: Arc-transitive graph; Abelian Cayley graph; Voltage graph; Bouquets.
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7
TitleA Short Note on Approximation Properties of q-Baskakov-Sz??sz-Stancu Operators
Vol.38(6) (2014) page: 857-871
Author(s): V.N. Mishra and P. Sharma  
Abstract:

In this paper, we introduce the q-analogue of Baskakov-Szász-Stancu operators. First, we use properties of q-calculus to estimate moments of these operators. We have estimated some approximation properties and asymptotic formula for these operators. In last section, we give better error estimations for said operators.


Keywords: Baskakov-Sz??sz-Stancu operators; q-calculus; Asymptotic formula; Rate of convergence of weighted spaces.
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8
TitlePartial ??-Semirings
Vol.38(6) (2014) page: 873-885
Author(s): S.M. Munnangi and D.S.P. Korrapati  
Abstract:

Usual addition can not be defined on the set of all partial functions over a set. We define a natural addition (disjoint-domain sum) and functional composition on them so that they form a partial Γ-semiring. We give several examples of partial Γ-semirings. Also congruence relations and quotients of partial Γ-semirings are studied.


Keywords: Partial ??-semirng; Diagonal property; Partial sub ??-semiring; ??-homomorp- hism and ??-congruence relation on partial ??-semirings.
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9
TitleAn Introduction to Operator Seminearrings of a Near-??-Semiring
Vol.38(6) (2014) page: 887-905
Author(s): S.K. Sardar and R. Mukherjee  
Abstract:

In order to study near-Γ-semirings the notion of operator seminearrings of a near-Γ-semiring are introduced. Then we obtain an inclusion preserving bijection between the set of all weak ideals of a near-Γ-semiring and that of its left operator seminearring. We also obtain an inclusion preserving bijection between the set of all ideals of a near-Γ-semiring and that of its left as well as right operator seminearrings. This result is applied to characterize different types of near-Γ-semirings such as Noetherian near-Γ-semiring, Artinian near-Γ-semiring and 0-simple near-Γ-semiring.


Keywords: Near-??-semiring; Operator seminearrings of a near-??-semiring; Noetherian near-??-semiring; Artinian near-??-semiring; 0-simple near-??-semiring.
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10
TitleConstruction of Certain Unit Regular Orthodox Submonoids
Vol.38(6) (2014) page: 907-916
Author(s): V.K. Sreeja and A.R. Rajan  
Abstract:

A regular semigroup S is said to bo orthodox if for any e,f ∈ E(S), ef ∈ E(S) where E(S) denotes the set of idempotents of S. A regular monoid S is said to be unit regular if for any x ∈ S , there exists an element u in the group of units of S such that x = xux . Here we characterize some orthodox unit regular submonoids associated with the L−class and R− class of a R −strongly (L−strongly) unit regular monoid.


Keywords: Orthodox unit regular monoid; R(L) strongly unit regular monoid; Subgroup; Maximal group; L− class; R− class.
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11
TitleUnicity of Entire Functions That Share One Value With Their Linear Differential Polynomials
Vol.38(6) (2014) page: 917-923
Author(s): X.Q. Wang, C.L. Lei and C.F. Chen  
Abstract:

Let f be a nonconstant entire function, let a be a finite nonzero complex number, and let L(f)=f(k)+ak−1f(k−1)+…+a1f′+a0f , where k ≥ 2 is a positive integer, aj(j=0,1,2,…,k−1) are constants. Suppose that f(z)=a ⇒ f′(z)=a, and f′(z)=a ⇒ L(f)(z)=L′(f)(z)=a. Then, if a0\noindentt = 1, then either f(z)=Ae\tfrac11−a0z+a  or  f(z)=Ae z, where A is a nonzero constant; if a0=1, then L(f)=f.


Keywords: Entire function; Differential polynomial; Uniqueness.
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12
TitleCoefficient Inequalities for Certain Classes of Sakaguchi -Type Harmonic Functions
Vol.38(6) (2014) page: 925-931
Author(s): E. Yaşar and S. Yalçın  
Abstract:

Let SH(α,s,t) be the class of normalized harmonic functions f=h+?Dg defined in the open unit disk satisfying

Re

\tfrac(s−t)
zh(z)−

zg(z)
 

h(sz)−h(tz)+

g(sz)
 

g(tz)
 
 

> α

for complex numbers s, t with s ≠ t and for α (0 ≤ α < 1). The main object of this paper is to obtain a necessary and sufficient convolution characterization and a sufficient coefficient condition for the class SH(α,s,t). Also, distortion bounds for the function f satisfying the coefficient condition are obtained.

 


Keywords: Entire function; Differential polynomial; Uniqueness.
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13
TitleContents for Volume 38
Vol.38(6) (2014) page: 933-936
Author(s):   
Abstract:

 


Keywords:
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