Browsing by Author "Alzabut, J. O."

Now showing 1 - 8 of 8

Citation - WoS: 21
Citation - Scopus: 18
Banach Contraction Principle for Cyclical Mappings on Partial Metric Spaces
(Springer international Publishing Ag, 2012) Mukheimer, A.; Zaidan, Y.; Abdeljawad, T.; Alzabut, J. O.
We prove that the Banacah contraction principle proved by Matthews in 1994 on 0-complete partial metric spaces can be extended to cyclical mappings. However, the generalized contraction principle proved by (Ilic et al. in Appl. Math. Lett. 24:1326-1330, 2011) on complete partial metric spaces can not be extended for cyclical mappings. Some examples are given to illustrate our results. Moreover, our results generalize some of the results obtained by (Kirk et al. in Fixed Point Theory 4(1):79-89, 2003). An Edelstein type theorem is also extended when one of the sets in the cyclic decomposition is 0-compact.
Citation - WoS: 17
Citation - Scopus: 13
Best Proximity Points for Cyclical Contraction Mappings With 0-Boundedly Compact Decompositions
(Eudoxus Press, Llc, 2013) Abdeljawad, Thabet; Abdeljawad, T.; Alzabut, J. O.; Alzabut, Jehad; Mukheimer, A.; Zaidan, Y.; Matematik
The existence of best proximity points for cyclical type contraction mappings is proved in the category of partial metric spaces. The concept of 0-boundedly compact is introduced and used in the cyclical decomposition. Some possible generalizations to the main results are discussed. Further, illustrative examples are given to demonstrate the effectiveness of our results.
Citation - WoS: 28
Citation - Scopus: 33
Existence of Periodic Solutions, Global Attractivity and Oscillation of Impulsive Delay Population Model
(Pergamon-elsevier Science Ltd, 2007) Alzabut, J. O.; Saker, S. H.
In this paper we consider the nonlinear impulsive delay population model. The main objective is to systematically study the qualitative behavior of the model including existence of periodic solutions, global attractivity and oscillation. The main oscillation results are the results of the prevalence of the mature cells about the periodic solutions and the global attractivity results are the conditions for nonexistence of dynamical diseases on the population. (c) 2006 Elsevier Ltd. All rights reserved.
Citation - WoS: 30
Citation - Scopus: 33
On Almost Periodic Solutions for an Impulsive Delay Logarithmic Population Model
(Pergamon-elsevier Science Ltd, 2010) Sermutlu, E.; Alzabut, J. O.; Stamov, G. Tr.
By employing the contraction mapping principle and applying the Gronwall-Bellman inequality, sufficient conditions are established to prove the existence and exponential stability of positive almost periodic solutions for an impulsive delay logarithmic population model. An example with its numerical simulations has been provided to demonstrate the feasibility of our results. (C) 2009 Elsevier Ltd. All rights reserved.
Citation - WoS: 15
Citation - Scopus: 16
Periodic Solutions, Global Attractivity and Oscillation of an Impulsive Delay Host-Macroparasite Model
(Pergamon-elsevier Science Ltd, 2007) Alzabut, J. O.; Saker, S. H.
In this paper we will consider the nonlinear impulsive delay host-macroparasite model with periodic coefficients. By means of the continuation theorem of coincidence degree, we establish a sufficient condition for the existence of a positive periodic solution M(t) with strictly positive components. Moreover, we establish a sufficient condition for the global attractivity of M(t) and some sufficient conditions for oscillation of all positive solutions about the positive periodic solution M(t). (c) 2006 Elsevier Ltd. All rights reserved.
Citation - WoS: 7
Citation - Scopus: 6
Perron's Theorem for Q-Delay Difference Equations
(Natural Sciences Publishing Corp-nsp, 2011) Alzabut, Jehad; Alzabut, J. O.; Abdeljawad, T.; Abdeljawad, Thabet; Matematik
In this paper, we prove that if a linear q-delay difference equation satisfies Perron's condition then its trivial solution is uniformly asymptotically stable.
Piecewise constant control of boundary value problem for linear impulsive differential systems
(2007) Alzabut, J. O.
A piecewise constant control that solves the boundary value problem for linear impulsive differential systems is considered. We establish a necessary and sufficient conditions for the existence of such control. Moreover, a result that explicitly characterizes the solving control is presented.
Citation - WoS: 33
Citation - Scopus: 34
Positive Almost Periodic Solutions for a Delay Logarithmic Population Model
(Pergamon-elsevier Science Ltd, 2011) Sermutlu, E.; Alzabut, J. O.; Stamov, G. T.
By utilizing the continuation theorem of coincidence degree theory, we shall prove that a delay logarithmic population model has at least one positive almost periodic solution. An example is provided to illustrate the effectiveness of the proposed result. (C) 2010 Elsevier Ltd. All rights reserved.