Volterra-Fredholm nonlinear systems with modified argument via weakly Picard operators theory

Author: Claudia Băcotiu

Abstract: In the present paper we consider the following system of nonlinear Volterra-Fredholm integral equations with modified argument: u(t; x) = g(t; x; u(t; x); u(0; a)) PDF |

General constructive fixed point theorems for Ciric-type almost contractions in metric spaces

Author: Vasile Berinde

Abstract: Existence and existence and uniqueness results for fixed points of single-valued Ciric almost contractions as well as convergence theorems for Picard iteration to these fixed points are proved. The Ciric type almost contraction condition appear to be one of the most general metrical condition for which the set of fixed points is not a singleton but the fixed points can be approximated by means of Picard iteration. Our results unify, generalize and extend most of the fundamental metrical fixed point theorems in literature (Banach, Kannan, Bianchini, Reich, Rus, Chatterjea, Rhoades, Hardy and Rogers, Zamfirescu, Ciric etc.) from the case of a unique fixed point to the case of non unique fixed points. PDF |

Abstract: For any Boolean algebra we prove a nice-looking recursive formula for the characteristic polynomial of its associated undirected Hasse graph, from which the computation of the spectrum smoothly follows. PDF |

System of integral equations with modified argument

Author: Maria Dobrițoiu

Abstract: For a system of nonlinear integral equations, we will use the Perov's theorem fixed point, general data dependence theorem and fiber generalized contraction theorem given by I. A. Rus, in order to establish the conditions concerning existence and uniqueness of the solution in Banach space C([a; b];Rm), the continuous data dependence of the solution and a theorem of differentiability of the solution with respect to parameters a and b. Two examples are also given here. PDF |

Abstract: The purpose of this paper to prove Baire's theorem and uniform limit theorem for L-fuzzy metric spaces. Also, we show every separable L-fuzzy metric spaces are second countable and subspace of a separable L-fuzzy metric space is separable. PDF |

On the global attractivity of difference equation of higher order

Author: E. M. Elabbasy / E. M. Elsayed

Abstract: In this paper we investigate the global convergence result and boundedness of solutions of the recursive sequence where the parameters a; b; c and d are positive real numbers and the initial values x PDF |

Positive solutions for nonlinear integral equations of Hammerstein type

Author: Andrei Horvat-Marc

Abstract: We apply a variant of Krasnoselskii's compression-expansion theorem for nonlinear operators which satisfy a compact condition of Monch type. Our approach makes possible to establish conditions which ensure the existence of positive solutions of abstract integral equations of Hammerstein type. PDF |

Random coincidence points of subcompatible multivalued maps with applications

Author: A. R. Khan / F. Akbar / N. Sultana

Abstract: The notion of subcompatible multivalued mapping is introduced. We present some random coincidence point and invariant approximation results for subcompatible random operators. Our work extends most of the important known results in the current literature to a new class of noncommuting multivalued mappings. We also develop random coincidence results for maps satisfying a more general contractive condition introduced by Ciric, Ume and Jesic [5]. PDF |

Anti-periodic solutions of functional difference equations with p-Laplacian

Author: Yuji Liu

Abstract: The p-Laplacian functional difference equation is studied. Three new existence results for anti-periodic solutions of the equation are established. PDF |

A new type of approximating sequence for the solution of the Cauchy problem consisting of piecewise linear functions

Author: Cristian Mortici / Emil Lungu

Abstract: This paper continues the study of a new successive approximation method for solving the Cauchy problem. The motivation for considering such a method consists in the fact that in practice real difficulties arise in the problem of computing integrals from the respective recurrence relations. We give below an original method to avoid these difficulties by defining a similar recurrence for solving the Cauchy problem, so that the obtaining approximating sequence consists in functions which are piecewise linear. We prove the (uniform) convergence and finally, a numerical example is given. PDF |

On the asymptotic behaviour of finite Markov chains

Author: Alina Nicolaie

Abstract: We give two sufficient conditions for weak and strong ergodicity of a nonhomogeneous finite Markov chain in terms of similar properties of a certain chain of smaller size. PDF |

An algorithm for solving nonsmooth variational inequalities arising in frictional quasistatic contact problems

Author: Nicolae Pop

Abstract: The aim of this paper is to give an algorithm for nonsmooth minimization using the generalized Jacobians with applications in contact problems. Some definitions, results and algorithms from non-smooth analysis are presented which lead to some sufficient conditions such that the nonlinear and nondifferentiable system obtained in modeling the contact problems with friction, have one solution which is obtained by bundle methods. PDF |

Abstract: The star graph has been known as an attractive model for interconnection networks due to its topological properties, capacity to simulate other basic network topologies and possibility to design efficient communication algorithms. In this paper we study the possibility to embed an array between any two nodes of a star graph and then we show that between any two nodes of a n-star graph there is a simple path that contains at least n! - 2 nodes. PDF |