... Extended contraction principle
We have the following generalized form of Banach’s contraction for cone metric spaces.
Theorem 3.1 see 11, Theorem 1. Let X, d be a complete cone metric space, ... fixed point.
Hindawi Publishing Corporation
Fixed Point Theory and Applications
Volume 2008, Article ID 768294, 11 pages
doi:10.1155/2008/768294
Research Article
Some E...
... fixed point of f and g.
2. Main Results
In this section we will prove some fixed point theorems of contractive mappings for cone
metric space. We generalize some results of 1–4 by omitting the ... called a cone metric on X,andX, d is called a cone metric space. The
concept of a cone metric space is more general than of a metric space.
Definition 1.2 see 2...
... Δ
J
denotes the face of Δ
n
corresponding to the subindex
of J in {0, 1, 2, ,n}.
12 Fixed Point Theory and Applications
by the same argument as in the proof of Theorem 4.1 in 16 that there exists ... U
0
of the origin in Z such that
F
a, y, z
∗
U
0
/
⊂C. 3.9
Since F is upper C-continuous, it follows that for any neighbourhood U of the origin in Z,
there exists a...
... Hindawi Publishing Corporation
Journal of Inequalities and Applications
Volume 2011, Article ID 531540, 10 pages
doi:10.1155/2011/531540
Research Article
Some Properties of Certain Class of
Integral ... obtained several inclusion relationships and integral-
preserving properties associated with some subclasses involving the operator Q
λ
α,β
, some sub-
ordination and superordi...
... Liu, Some applications of certain integral operator,” Kyungpook Mathematical Journal, vol. 43, no.
2, pp. 211–219, 2003.
9 H. Saitoh, “A linear operator and its applications to certain subclasses ... Complex Analysis, vol. 1013 of Lecture Notes in
Mathematics, pp. 362–372, Springer, Berlin, Germany, 1983.
11
I. S. Jack, “Functions starlike and convex of order α,” Journal of th...
... Bernstein
polynomials.
In the present paper, we introduce the Bernstein polynomials on the ring of p-adic
integers Z
p
. We also investigate some interesting properties of the Bernstein polynomials
related ... the integral of the product of several type Bernstein
polynomials,” IST Transaction of Applied Mathematics-Modelling and Simulation. In press.
2 M. Acikgoz and S. Arac...
... center of the ball B.
We omit the proof since it is the same as the proof of Theorem 3.2.
8 Journal of Inequalities and Applications
Proof. First, by using the H
¨
older inequality and inequality ... the
composition of the three operators under the consideration to certain harmonic forms and to
obtain some estimates for certain integrals which are useful in studying the properties...
... Govil
Making use of the principle of subordination between analytic functions and a family of integral
operators defined on the space of meromorphic functions, we introduce and investigate some
new ... ψ
.
2.23
Proof. In view of 1.26 and Theorem 2.3, and by similarly applying the method of proof of
Theorem 2.2, we conclude that the assertion of Theorem 2.4 holds.
3....
... generalization of Lemma 2.2 in 10. The proof of Lemma 2.6 is
quite different from its proof. Actually, the proof of Lemma 2.2 in 10 is incorrect. The main
problem appears at 2.2 in 10.Sincef has ... 0,
4.1
for some ξ
0
∈ .
We can arrive at a contradiction by using the same argument as in the latter part of
proof of Theorem 1.1.
This completes the proof of Theore...