Journal of Nonlinear Analysis and Optimization: Theory & Applications (JNAO)

THE EIGENVALUE PROBLEMS FOR DIFFERENTIAL PENCILS ON THE HALF LINE

A. Neamaty — 2012-05-08

In this paper we study the solution of the boundary value problem for second-order differential operator on the half-line having jump point in an interior point. Using of the fundamental system of solutions, we investigate the asymptotic distribution of eigenvalues.

FIXED POINT THEOREMS IN SYMMETRIC 2-CONE BANACH SPACE $(\ell_p, \|\cdot\|^c_p)$

A. Sahiner — 2012-05-08

The present article is concerned with $l_p$ sequences spaces in point of its symmetric 2-cone norm structure. Further, fixed point theorem for this space is proved.

COAPPROXIMATION IN PROBABILISTIC NORMED SPACES

A. Khorasani — 2012-05-08

In this article, we studied the best coapproximation in probabilistic 2-normed spaces. We defined the best coapproximation on these spaces and generalized some definitions such as set of best coapproximation, $P_b$-coproximinal set and $P_b$-coapproximately compact and orthogonality relative to any set and proved some theorems about them.

SOME NOTES ON $(\alpha, \beta)$-GENERALIZED HYBRID MAPPINGS

H. Afshari — 2012-05-08

In 1973, Bruck generalized the notion nonexpansive mappings by introducing firmly nonexpansive mappings. Kohsaka and Takahashi introduced nonspreading mappings in 2010. But, each nonexpansive mapping is a 1-hybrid mapping and each nonspreading mapping is a 0-hybrid mapping. Thus, the notion of $\lambda$-hybrid mappings is a generalization of the notions of firmly nonexpansive mappings and nonspreading mappings. In 2011, Takahashi introduced generalized hybrid mappings and proved some weak convergence theorems for generalized hybrid mappings in Banach spaces. On the other hand, Aoyama and Kohsaka introduced $\alpha$-nonexpansive mappings on Banach spaces in 2011 and proved some fixed point theorems for the mappings. Also, Kocourek, Takahashi and Yao provided the notions of $(\alpha, \alpha-1)$-generalized hybrid mappings and $(\alpha, \beta, \gamma)$-super hybrid mappings in 2011. In this paper, we give some results on $(\alpha, \beta)$-generalized hybrid mapping. Also, by using and combining ideas of some recent papers, we generalize the notion of $\alpha$-nonexpansivity to $(\alpha, \beta)$-nonexpansivity and give some results about the subject.

ON A HALF-DISCRETE REVERSE MULHOLLAND'S INEQUALITY

B. Yang — 2012-05-08

By using the way of weight functions and the technique of real analysis, a half-discrete reverse Mulholland's Inequality with a best constant factor is given. The extension with multi-parameters and the equivalent forms are also considered.

ON SOME I-CONVERGENT SEQUENCE SPACES DEFINED BY A SEQUENCE OF MODULI

V.A. Khan — 2012-05-08

In this article we introduce the sequence spaces $c_0^I(F), c^I (F)$ and $\ell_\infty(F)$ for the sequence of modulii $F = (f_k)$ and study some of the properties of these spaces. The results here in proved are analogus to those by Vakeel.A.Khan and Khalid Ebadullah (Theory and Applications of Mathematics and Computer Science,1(2)(2012)22-30.)

FIXED POINT THEOREMS IN NON-ARCHIMEDEAN MENGER PM-SPACES

S. L. Singh — 2012-05-08

Recently, Sintunavarat and Kumam [Common fixed point theorems for a pair of weakly compatible mappings in fuzzy metric spaces, J. Appl. Math. vol. 2011, Article ID 637958, 14 pages, 2011] defined the notion of (CLRg) property which is more general than (E.A) property. In the present paper, we prove a common fixed point theorem for a pair of weakly compatible mappings in Non-Archimedean Menger PM-spaces using (CLRg) property. As an application to our main result, we present a common fixed point theorem for two finite families of self mappings. Our results improve and extend several known results existing in the literature.

COMMON FIXED POINT THEOREM IN INTUITIONISTIC FUZZY METRIC SPACE UNDER (S-B) PROPERTY

P. K. Sharma — 2012-05-18

The main purpose of this paper is to give common fixed point theorem in intuitionistic fuzzy metric space under strict contractive conditions for mappings satisfying (S-B) property

PICARD AND ADOMIAN DECOMPOSITION METHODS FOR A COUPLED SYSTEM OF QUADRATIC INTEGRAL EQUATIONS

A. M. A. El-sayed — 2012-05-29

The comparison between the classical method of successive approximations (Picard) method and Adomian decomposition method was studied in many papers for example ([15] and [37]). In this paper we are concerning with two analytical methods; the classical method of successive approximations (Picard) [18] and Adomian decomposition methods ([1]-[6], [16] and [17]) for a coupled system of quadratic integral equations of fractional order. Also, the existence and uniqueness of the solution and the convergence will be discussed for each method and some examples will be studied.

ON SOME PROPERTIES OF P-WAVELET PACKETS VIA THE WALSH-FOURIER TRANSFORM

F. A. Shah — 2012-08-20

A novel method for the construction of orthogonal $p$-wavelet packets on a positive half-line R+ was given by the author in [Construction of wavelet packets on $p$-adic field, Int. J. Wavelets Multiresolut. Inf. Process., 7(5) (2009), pp. 553-565]. In this paper, we investigate their properties by means of the Walsh-Fourier transform. Three orthogonal formulas regarding these p-wavelet packets are derived.

CONTINUITY OF FUZZY TRANSITIVE ORDERED SETS

F. M. Zeyada — 2012-08-20

In the present paper we introduce and study the continuity for a set equipped with a transitive fuzzy binary order relation which we call a f-toset. Our work is inspired by the slogan: "Order theory is the study of transitive relations" due to S. Abramsky and A.Jung [1].

AN OTHER APPROACH FOR THE PROBLEM OF FINDING A COMMON FIXED POINT OF A FINITE FAMILY OF NONEXPANSIVE MAPPINGS

T. M. Tuyen — 2012-05-08

The purpose of this paper is to give a Tikhonov regularization method and some regularization inertial proximal point algorithm for the problem of finding a common fixed point of a finite family of nonexpansive mappings in an uniformly convex and uniformly smooth Banach space E, which admits a weakly sequentially continuous normalized duality mapping j from E to E^*.

ON THE SEMILOCAL CONVERGENCE OF ULM'S METHOD

I. K. Argyros — 2012-08-03

We provide sufficient convergence conditions for the semilocal convergence of Ulm's method [9] to a locally unique solution of an equation in a Banach space setting. Our results compare favorably to recent ones by Ezquerro and Hernández [3] which have improved earlier ones [4], [6]-[10], since under the same computational cost we provide: larger convergence domain; finer error bounds on the distances involved, and an at least as precise information on the location of the solution.

FIXED POINT THEOREMS IN MENGER SPACES USING THE $(CLR_{ST})$ PROPERTY AND APPLICATIONS

M. Imdad — 2012-08-03

In the present paper, we prove a common fixed point theorem for two pairs of weakly compatible mappings in Menger space employing the $(CLR_{ST})$ property. Some examples are furnished which demonstrate the validity of the hypotheses and degree of generality of our results. We extend our main result to four finite families of self mappings. As applications to our results, we obtain the corresponding common fixed point theorems in metric spaces. Our results improve and extend the results of Cho et al. [4] and Pathak et al. [21] besides several known results.

POSITIVE SOLUTIONS FOR FRACTIONAL DIFFERENTIAL EQUATIONS WITH P-LAPLACIAN

N. Nyamoradi — 2012-08-29

In this paper, we study the existence of positive solution to boundary value problem for fractional differential equation with a one-dimensional $p$-Laplacian operator
\begin{equation*}
begin{cases}
D_{0^+}^\sigma (\phi_p ( u'' (t))) - g (t) f (u (t)) = 0, t \in (0, 1),\\
\phi_p ( u'' (0)) = \phi_p ( u'' (1)) = 0,\\
a u (0) - b u' (0) = \sum_{i = 1}^{m - 2} a_i u (\xi_i),\\
c u (1) + d u' (1) = \sum_{i = 1}^{m - 2} b_i u (\xi_i),
\end{cases}
\end{equation*}
where $D_{0^+}^\alpha$ is the Riemann-Liouville fractional derivative of order $1 < \sigma \leq 2$, $\phi_p (s) = |s|^{p - 2} s$, $p > 1$ and $f$ is a lower semi-continuous function. By using Krasnoselskii's fixed point theorems in a cone, the existence of one positive solution and multiple positive solutions for nonlinear singular boundary value problems is obtained.

ON SET-VALUED MIXED VECTOR VARIATIONAL-LIKE INEQUALITIES IN BANACH SPACES

S. A. Khan — 2012-08-28

In this paper we introduce the concept of generalized $\eta$-pseudomonotone mappings and generalized version of vector mixed variational-like inequalities in Banach spaces. Utilizing Ky Fan's Lemma and Nadler's Lemma, we derive the solvability for this class of vector mixed variational-like inequalities involving generalized $\eta$-pseudomonotone mappings. The results presented in this work are extensions and improvements of some earlier and recent results in the literature.

BEST APPROXIMATION FOR CONVEX SUBSETS OF 2-INNER PRODUCT SPACES

M. Abrishasmi-moghaddam — 2012-09-30

In this paper, we study the concept of best approximation in 2-inner product spaces. We get some characteristic theorems for the elements of best approximation for convex subsets of 2-inner product spaces. Finally we get some properties of the metric projection map in this spaces.

A GENERAL ITERATIVE ALGORITHM FOR MONOTONE OPERATORS AND FIXED POINT PROBLEMS IN HILBERT SPACES

A.R. Medghalchi — 2012-09-09

Let $VI(A,H)$ be the set of all solutions of the following variational inequality problem: $$\text{$\hspace{.6cm}$ find $\hspace{.125cm}u\in H \hspace{.125cm}$ such that $\langle v-u,Au\rangle\geq0,\hspace{.4cm}$for all $v\in H.$}$$ Where $H$ is a Hilbert space, $A:H\rightarrow H$ is a Lipschitz continuous and monotone operator.
Assume that $F:H\rightarrow H$ is a Lipschitz continuous and strongly monotone operator. Let $f:H\rightarrow H$ be a Lipschitz continuous mapping. In this paper, we consider a demiclosed, demicontractive mapping $T$ on $H$ such that $Fix(T)\cap VI(A,H)\neq\varnothing.$ For finding an element $x^{\ast}$ which solves the following variational inequality problem: find an $x^{\ast}\in Fix(T)\cap VI(A,H)$ such that
$$\text{ $\langle v-x^{\ast},\mu Fx^{\ast}-\gamma fx^{\ast}\rangle\geq0,\hspace{.5cm}$for all $v\in Fix(T)\cap VI(A,H),$}$$ when $\mu$ and $\gamma$ are positive real numbers which satisfy appropriate conditions, we introduce a new general iterative algorithm and obtain strong convergence results.

A RELATED FIXED POINT THEOREM IN $n$ COMPLETE FUZZY METRIC SPACES

F. Merghadi — 2012-09-03

We prove a related fixed point theorem for $n$ mappings in $n$ fuzzy metric spaces using an implicit relation which generalizes results of Aliouche and Fisher [1] and Rao et al. [13].