Browsing by Author "Abdeljawad, Thabet"

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Citation - WoS: 16
Citation - Scopus: 20
Common Fixed Point Theorems in Cone Banach Spaces
(Hacettepe Univ, Fac Sci, 2011) Abdeljawad, Thabet; Karapinar, Erdal; Tas, Kenan; Mathematics; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
Recently, E. Karapinar (Fixed Point Theorems in Cone Banach Spaces, Fixed Point Theory Applications, Article ID 609281, 9 pages, 2009) presented some fixed point theorems for self-mappings satisfying certain contraction principles on a cone Banach space. Here we will give some generalizations of this theorem.
Citation - WoS: 43
Coupled Fixed Points for Meir-Keeler Contractions in Ordered Partial Metric Spaces
(Hindawi Ltd, 2012) Abdeljawad, Thabet; Aydi, Hassen; Karapinar, Erdal; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
In this paper, we prove the existence and uniqueness of a new Meir-Keeler type coupled fixed point theorem for two mappings F : X x X -> X and g : X -> X on a partially ordered partial metric space. We present an application to illustrate our obtained results. Further, we remark that the metric case of our results proved recently in Gordji et al. (2012) have gaps. Therefore, our results revise and generalize some of those presented in Gordji et al. (2012)
Citation - WoS: 16
A Gap in the Paper "a Note on Cone Metric Fixed Point Theory and Its Equivalence" [nonlinear Anal. 72(5), (2010), 2259-2261]
(Gazi Univ, 2011) Abdeljawad, Thabet; Karapinar, Erdal; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
There is a gap in Theorem 2.2 of the paper of Du [1]. In this paper, we shall state the gap and repair it.
Citation - WoS: 79
Citation - Scopus: 82
A Generalized Contraction Principle With Control Functions on Partial Metric Spaces
(Pergamon-elsevier Science Ltd, 2012) Abdeljawad, Thabet; Karapinar, Erdal; Tas, Kenan; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
Partial metric spaces were introduced by Matthews in 1994 as a part of the study of denotational semantics of data flow networks. In this article, we prove a generalized contraction principle with control functions phi and psi on partial metric spaces. The theorems we prove generalize many previously obtained results. We also give some examples showing that our theorems are indeed proper extensions. (C) 2011 Elsevier Ltd. All rights reserved.
Citation - WoS: 34
Citation - Scopus: 42
Lyapunov-Type Inequalities for Mixed Non-Linear Forced Differential Equations Within Conformable Derivatives
(Springer, 2018) Abdeljawad, Thabet; Agarwal, Ravi P.; Alzabut, Jehad; Jarad, Fahd; Ozbekler, Abdullah; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
We state and prove new generalized Lyapunov-type and Hartman-type inequalities fora conformable boundary value problem of order alpha is an element of (1,2] with mixed non-linearities of the form ((T alpha X)-X-a)(t) + r(1)(t)vertical bar X(t)vertical bar(eta-1) X(t) + r(2)(t)vertical bar x(t)vertical bar(delta-1) X(t) = g(t), t is an element of (a, b), satisfying the Dirichlet boundary conditions x(a) = x(b) = 0, where r(1), r(2), and g are real-valued integrable functions, and the non-linearities satisfy the conditions 0 < eta < 1 < delta < 2. Moreover, Lyapunov-type and Hartman-type inequalities are obtained when the conformable derivative T-alpha(a) is replaced by a sequential conformable derivative T-alpha(a) circle T-alpha(a), alpha is an element of (1/2,1]. The potential functions r(1), r(2) as well as the forcing term g require no sign restrictions. The obtained inequalities generalize some existing results in the literature.
Citation - WoS: 57
Citation - Scopus: 57
Quasicone Metric Spaces and Generalizations of Caristi Kirk's Theorem
(Springer international Publishing Ag, 2009) Abdeljawad, Thabet; Karapinar, Erdal; Mathematics; 02. School of Arts and Sciences; 01. Atılım University
Cone-valued lower semicontinuous maps are used to generalize Cristi-Kirik's fixed point theorem to Cone metric spaces. The cone under consideration is assumed to be strongly minihedral and normal. First we prove such a type of fixed point theorem in compact cone metric spaces and then generalize to complete cone metric spaces. Some more general results are also obtained in quasicone metric spaces. Copyright (C) 2009 T. Abdeljawad and E. Karapinar.