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Online Edition: ISSN 1843 - 4401

Carpathian J. Math. is a category A journal in the CNCSIS classification

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Contents (PDF)
Vol. 30 (2014), No. 2, 15 September 2014
Fixed points of set-valued contractions in partial metric spaces endowed with a graph
Author: Mujahid Abbas / Basit Ali / Gabriela Petrușel
Abstract: Hassen, Abbas and Vetro [H. Aydi, M. Abbas and C. Vetro, Partial Hausdorff metric and Nadler's fixed point theorem on partial metric spaces, Topology and its App., 159 (2012), 3234--3242] introduced the concept of a partial Hausdorff-Pompeiu metric and proved Nadler's theorem in this context. Employing the notion of a partial Hausdorff-Pompeiu metric, we investigate the existence of fixed points of set-valued mappings on partial metric spaces endowed with a graph. Our results extend some recent theorems in the literature.
No. of downloads: 298
Asymptotic expansions for the ratio of gamma functions
Author: Chao-Ping Chen / Long Lin
Abstract: The main object of this paper is to establish a class of the asymptotic expansions for the ratio of gamma functions $\frac{\Gamma(x+1)}{\Gamma(x+\frac{1}{2})}$, by mainly using Bell polynomials and the partition function. This unifies several approximation formulas for the ratio of gamma functions due to Mortici.
No. of downloads: 229
Some results of differentiability for the solution of an integral equations system
Author: Maria Dobrițoiu
Abstract: Using the fixed point theorem given by [Rus, I. A., A Fiber generalized contraction theorem and applications, Mathematica, 41(64) (1999), No. 1, 85--90] and an idea of [Sotomayor, J., Smooth dependence of solution of differential equation on initial data: a simple proof, Bol. Soc. Brasil., 4 (1973), No. 1, 55--59] we establish some conditions of differentiability of the solution for the following system of integral equations: \begin{equation*} x(t)=\int\limits_{a}^{b}K(t,s)\cdot h(s,x(s),x(a),x(b))ds+f(t),\;t\in \lbrack a ,b ], \end{equation*} and such we obtain two theorems of differentiability. Finally, two examples are given.
No. of downloads: 221
Multivalued representation and new algebraic structures for fuzzy numbers
Author: Dorina Fechete / Ioan Fechete
Abstract: In this paper we introduce a new representation of fuzzy numbers (called the multivalued representation) and a new multiplication on the set $\mathfrak{F}$ of fuzzy numbers. Introducing a Dorroh type product between fuzzy numbers, we construct some semiring structures on the set $\mathfrak{F}$. Two important particular cases of the general Dorroh type product are the cross product, introduced in [Ban, A. I. and Bede, B., Properties of the cross product of fuzzy numbers, Journal of Fuzzy Mathematics, 14 (2006), 513--531] and the Dorroh product, introduced in this paper. An equivalence relation, compatible with the addition and the Dorroh product, is also given.
No. of downloads: 208
Existence and approximation of fixed points in convex metric spaces
Author: Hafiz Fukhar-Ud-Din
Abstract: A fixed point theorem for a generalized nonexpansive mapping is established in a convex metric space introduced by Takahashi [A convexity in metric spaces and nonexpansive mappings, Kodai Math. Sem. Rep., 22 (1970), 142--149]. Our theorem generalizes simultaneously the fixed point theorem of Bose and Laskar [Fixed point theorems for certain class of mappings, Jour. Math. Phy. Sci., 19 (1985), 503--509] and the well-known fixed point theorem of Goebel and Kirk [A fixed point theorem for asymptotically nonexpansive mappings, Proc. Amer. Math. Soc., 35 (1972), 171--174] on a nonlinear domain. The fixed point obtained is approximated by averaging Krasnosel'skii iterations of the mapping. Our results substantially improve and extend several known results in uniformly convex Banach spaces and $CAT(0)$ spaces.
No. of downloads: 215
Semi-linear fractional systems with Caputo type multi-step differences
Author: Ewa Girejko / Dorota Mozyrska
Abstract: A new class of fractional linear and semi-linear discrete-time systems described by the collection of state equations is introduced. The solution to the system is derived by the recursive formula. Presented results concern the fractional $h$-difference operator.
No. of downloads: 174
Fixed points for $\alpha$-$\psi$-Suzuki contractions with applications to integral equations
Author: N. Hussain / P. Salimi / P. Vetro
Abstract: Recently, Suzuki [Proc. Amer. Math. Soc. 136 (2008), 1861--1869] proved a fixed point theorem that is a generalization of the Banach contraction principle and characterized the metric completeness. Paesano and Vetro [Topology Appl., 159 (2012), 911--920] proved an analogous fixed point result on a partial metric space. In this paper we prove some fixed point results for Suzuki-$\alpha$-$\psi$-contractions and Suzuki-$\varphi_\theta$-$\psi_r$-contractions on a complete partially ordered metric space. Moreover, some examples and an application to integral equations are provided to illustrate the usability of the obtained results.
No. of downloads: 192
On the $L^\infty$-uniqueness of multidimensional Nelson's diffusion
Author: Ludovic Dan Lemle
Abstract: In this paper we study the uniqueness in the sense of the essential self-adjointness for the generator of Nelson's diffusion on $L^\infty$. As consequence it is obtained the $L^1$-uniqueness of weak solutions for the associated Fokker-Planck-Kolmogorov equation.
No. of downloads: 160
Operators commuting with multi-parameter shift semigroups
Author: Oleh Lopushansky / Sergii Sharyn
Abstract: Using operators of cross-correlation with ultradistributions supported by a positive cone, we describe a commutative algebra of shift-invariant continuous linear operators, commuting with contraction multi-parameter semigroups over a Banach space. Thereby, we generalize classic Schwartz's and Hormander's theorems on shift-invariant operators.
No. of downloads: 206 Full access PDF |
Baer-Galois connections]{Baer-Galois connections and applications
Author: Gabriela Olteanu
Abstract: We define Baer-Galois connections between bounded modular lattices. We relate them to lifting lattices and we show that they unify the theories of (relatively) Baer and dual Baer modules.
No. of downloads: 189
Customized orthogonalization via deflation algorithm with applications in face recognition
Author: Lăcrămioara (Liță) Grecu / Elena Pelican
Abstract: The face recognition problem is a topical issue in computer vision. In this paper we propose a customized version of the orthogonalization via deflation algorithm to tackle this problem. We test the new proposed algorithm on two datasets: the well-known ORL dataset and an own face dataset, CTOVF; also, we compare our results (in terms of rate recognition and average quiery time) with the outcome of a standard algorithm in this class (dimension reduction methods using numerical linear algebra tools).
No. of downloads: 167
Remarks on a new metric in the unity disc of the complex plane
Author: Laurian-Ioan Pișcoran / Cătălin Barbu
Abstract: The curvature $K$ of an surface depends only to the surface metric and so is an intrinsic invariant. In this paper we will study a new metric in the unity complex disc, which is connected to the well-known Poincar'e metric used in hyperbolic geometry.
No. of downloads: 181
Morphic bimodules and rings
Author: Lavinia Pop
Abstract: Morphic bimodules and morphic rings are defined and studied. Several special classes of morphic rings with involutions and modules over skew group rings are also discussed.
No. of downloads: 170
On the Maksa-Volkmann functional inequality $\left\vert f\left( x+y\right) \right\vert \geq \left\vert f\left( x\right) +f\left( y\right) \right\vert $ when the range of $f$ is a space of functions
Author: Marius Rădulescu / Sorin Rădulescu
Abstract: P. Volkmann functional inequality $\left\vert f\left( x+y\right) \right\vert \geq \left\vert f\left( x\right) +f\left( y\right) \right\vert $ is extended to functions $f:G\rightarrow \mathfrak{F}\left( X,E\right) $ where $G$ is an additive group and $\mathfrak{F}\left( X,E\right) $ is the space of functions from a set $X$ to a linear normed space $E$. As a corollary one proves that an operator $T:C\left( X,K\right) \rightarrow C\left( X,K\right) $ which satisfies the functional inequality $\left\vert T\left( f+g\right) \right\vert \geq \left\vert T\left( f\right) +T\left( g\right) \right\vert $ , $f,g\in C\left( X,K\right) $ is additive. Here we denoted by $X$ a compact topological space, $K$ is $\mathbb{R}$ or $\mathbb{C}$ and $C\left( X,K\right) $ is the linear space of continuous functions defined on $X$ with values in $K$.
No. of downloads: 160
Solutions of variational inequality problems in the set of fixed points of pseudocontractive mappings
Author: Habtu Zegeye / Nasser Shahzad
Abstract: We introduce an iterative process which converges strongly to a solution of the variational inequality problems for $\eta$-inverse strongly accretive mappings in the set of fixed points of pseudocontractive mappings. Our theorems improve and unify most of the results that have been proved for this important class of nonlinear operators.
No. of downloads: 222

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