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. PDF |

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. PDF |

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. PDF |

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. PDF |

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. PDF |

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. PDF |

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. PDF |

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. PDF |

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. 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. PDF |

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). PDF |

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. PDF |

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. PDF |

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 $K$. PDF |

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. PDF |