Browsing by Author "Shahzad, Naseer"
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Article Citation Count: 27Discussion of coupled and tripled coincidence point theorems for φ-contractive mappings without the mixed g-monotone property(Springer international Publishing Ag, 2014) Karapınar, Erdal; Roldan, Antonio; Shahzad, Naseer; Sintunavarat, Wutiphol; MathematicsAfter the appearance of Ran and Reuring's theorem and Nieto and Rodriguez-Lopez's theorem, the field of fixed point theory applied to partially ordered metric spaces has attracted much attention. Coupled, tripled, quadrupled and multidimensional fixed point results has been presented in recent times. One of the most important hypotheses of these theorems was the mixed monotone property. The notion of invariant set was introduced in order to avoid the condition of mixed monotone property, and many statements have been proved using these hypotheses. In this paper we show that the invariant condition, together with transitivity, lets us to prove in many occasions similar theorems to which were introduced using the mixed monotone property.Article Citation Count: 15Fixed point theorems in new generalized metric spaces(Springer Basel Ag, 2016) Karapınar, Erdal; O'Regan, Donal; Roldan Lopez de Hierro, Antonio Francisco; Shahzad, Naseer; MathematicsThe aim of our paper is to present new fixed point theorems under very general contractive conditions in generalized metric spaces which were recently introduced by Jleli and Samet in [Fixed Point Theory Appl. 2015 (2015), doi:10.1186/s13663-015-0312-7]. Although these spaces are not endowed with a triangle inequality, these spaces extend some well known abstract metric spaces (for example, b-metric spaces, Hitzler-Seda metric spaces, modular spaces with the Fatou property, etc.). We handle several types of contractive conditions. The main theorems we present involve a reflexive and transitive binary relation that is not necessarily a partial order. We give a counterexample to a recent fixed point result of Jleli and Samet. Our results extend and unify recent results in the context of partially ordered abstract metric spaces.Article Citation Count: 9On some fixed point theorems under (α, ψ, φ)-contractivity conditions in metric spaces endowed with transitive binary relations(Springer international Publishing Ag, 2015) Karapınar, Erdal; Karapinar, Erdal; Roldan-Lopez-de-Hierro, Antonio-Francisco; MathematicsAfter the appearance of Nieto and Rodriguez-Lopez's theorem, the branch of fixed point theory devoted to the setting of partially ordered metric spaces have attracted much attention in the last years, especially when coupled, tripled, quadrupled and, in general, multidimensional fixed points are studied. Almost all papers in this direction have been forced to present two results assuming two different hypotheses: the involved mapping should be continuous or the metric framework should be regular. Both conditions seem to be different in nature because one of them refers to the mapping and the other one is assumed on the ambient space. In this paper, we unify such different conditions in a unique one. By introducing the notion of continuity of a mapping from a metric space into itself depending on a function alpha, which is the case that covers the partially ordered setting, we extend some very recent theorems involving control functions that only must be lower/upper semi-continuous from the right. Finally, we use metric spaces endowed with transitive binary relations rather than partial orders.Article Citation Count: 16Remarks on 'Coupled coincidence point results for a generalized compatible pair with applications'(Springer international Publishing Ag, 2014) Erhan, İnci; Karapinar, Erdal; Karapınar, Erdal; Shahzad, Naseer; MathematicsVery recently, Hussain et al. (Fixed Point Theory Appl. 2014:62, 2014) announced the existence and uniqueness of some coupled coincidence point. In this short note we remark that the announced results can be derived from the coincidence point results in the literature.Article Citation Count: 0Some remarks about the existence of coupled g-coincidence points(Springeropen, 2015) Erhan, İnci; Roldan-Lopez-de-Hierro, Antonio-Francisco; Shahzad, Naseer; MathematicsVery recently, in a series of subsequent papers, Nan and Charoensawan introduced the notion of g-coincidence point of two mappings in different settings (metric spaces and G-metric spaces) and proved some theorems in order to guarantee the existence and uniqueness of such kind of points. Although their notion seems to be attractive, in this paper, we show how this concept can be reduced to the unidimensional notion of coincidence point, and how their main theorems can be seen as particular cases of existing results. Moreover, we prove that the proofs of their main statements have some gaps.Article Some remarks about the existence of coupled g-coincidence points(Journal of Inequalities and Applications, 2015) Erhan, İnci; Shahzad, Naseer; MathematicsVery recently, in a series of subsequent papers, Nan and Charoensawan introduced the notion of g-coincidence point of two mappings in different settings (metric spaces and G-metric spaces) and proved some theorems in order to guarantee the existence and uniqueness of such kind of points. Although their notion seems to be attractive, in this paper, we show how this concept can be reduced to the unidimensional notion of coincidence point, and how their main theorems can be seen as particular cases of existing results. Moreover, we prove that the proofs of their main statements have some gaps.Article Citation Count: 7The Study of Fixed Point Theory for Various Multivalued Non-Self-Maps(Hindawi Ltd, 2013) Karapınar, Erdal; Karapinar, Erdal; Shahzad, Naseer; MathematicsThe basic motivation of this paper is to extend, generalize, and improve several fundamental results on the existence (and uniqueness) of coincidence points and fixed points for well-known maps in the literature such as Kannan type, Chatterjea type, Mizoguchi-Takahashi type, Berinde-Berinde type, Du type, and other types from the class of self-maps to the class of non-self-maps in the framework of the metric fixed point theory. We establish some fixed/coincidence point theorems for multivalued non-self-maps in the context of complete metric spaces.