Browsing by Author "Roldan-Lopez-de-Hierro, Antonio-Francisco"

Now showing 1 - 18 of 18

Citation - WoS: 27
Citation - Scopus: 32
Coincidence Point Theorems in Quasi-Metric Spaces Without Assuming the Mixed Monotone Property and Consequences in g-metric Spaces
(Springer international Publishing Ag, 2014) Roldan-Lopez-de-Hierro, Antonio-Francisco; Karapinar, Erdal; de la Sen, Manuel; Mathematics
In this paper, we present some coincidence point theorems in the setting of quasi-metric spaces that can be applied to operators which not necessarily have the mixed monotone property. As a consequence, we particularize our results to the field of metric spaces, partially ordered metric spaces and G-metric spaces, obtaining some very recent results. Finally, we show how to use our main theorems to obtain coupled, tripled, quadrupled and multidimensional coincidence point results.
Citation - WoS: 169
Citation - Scopus: 183
Coincidence Point Theorems on Metric Spaces via Simulation Functions
(Elsevier Science Bv, 2015) Roldan-Lopez-de-Hierro, Antonio-Francisco; Karapinar, Erdal; Roldan-Lopez-de-Hierro, Concepcion; Martinez-Moreno, Juan; Mathematics
Due to its possible applications, Fixed Point Theory has become one of the most useful branches of Nonlinear Analysis. In a very recent paper, Khojasteh et al. introduced the notion of simulation function in order to express different contractivity conditions in a unified way, and they obtained some fixed point results. In this paper, we slightly modify their notion of simulation function and we investigate the existence and uniqueness of coincidence points of two nonlinear operators using this kind of control functions. (C) 2014 Elsevier B.V. All rights reserved.
Citation - WoS: 39
Citation - Scopus: 50
Discussion on Generalized-(αψ, Βφ)-Contractive Mappings Via Generalized Altering Distance Function and Related Fixed Point Theorems
(Hindawi Ltd, 2014) Berzig, Maher; Karapinar, Erdal; Roldan-Lopez-de-Hierro, Antonio-Francisco; Mathematics
We extend the notion of (alpha psi, beta phi)-contractive mapping, a very recent concept by Berzig and Karapinar. This allows us to consider contractive conditions that generalize a wide range of nonexpansive mappings in the setting of metric spaces provided with binary relations that are not necessarily neither partial orders nor preorders. Thus, using this kind of contractive mappings, we show some related fixed point theorems that improve some well known recent results and can be applied in a variety of contexts.
Citation - WoS: 1
DISCUSSION ON THE EQUIVALENCE OF W-DISTANCES WITH Ω-DISTANCES
(Yokohama Publ, 2015) Roldan-Lopez-de-Hierro, Antonio-Francisco; Karapinar, Erdal; Mathematics
In this manuscript, we study some relationships between w-distances on metric spaces and Omega-distances on G*-metric spaces. Concretely we show that the class of all w-distances on metric spaces is a subclass of all Omega-distances on G*-metric spaces. Then, researchers must be careful because some recent results about w-distances (for instances, in the topic of fixed point theory) can be seen as simple consequences of their corresponding results about Omega-distances. In this sense, we show how to translate some results between different metric models.
Citation - WoS: 9
Citation - Scopus: 8
Existence and Uniqueness of Best Proximity Points Under Rational Contractivity Conditions
(Walter de Gruyter Gmbh, 2016) Karapinar, Erdal; Roldan-Lopez-de-Hierro, Antonio-Francisco; Sadarangani, Kishin; Mathematics
The main aim of this paper is to present some theorems in order to guarantee existence and uniqueness of best proximity points under rational contractivity conditions using very general test functions. To illustrate the variety of possible test functions, we include some examples of pairs of functions which are included in innovative papers published in the last years. As a consequence, we prove that our results unify and extend some recent results in this field.
Citation - WoS: 3
Citation - Scopus: 3
An Illusion: "a Suzuki Type Coupled Fixed Point Theorem"
(Hindawi Publishing Corporation, 2014) Alsulami, Hamed H.; Karapinar, Erdal; Kutbi, Marwan A.; Roldan-Lopez-de-Hierro, Antonio-Francisco; Mathematics
We admonish to be careful on studying coupled fixed point theorems since most of the reported fixed point results can be easily derived from the existing corresponding theorems in the literature. In particular, we notice that the recent paper [Semwal and Dimri (2014)] has gaps and the announced result is false. The authors claimed that their result generalized the main result in [Doric and Lazovic (2011)] but, in fact, the contrary case is true. Finally, we present a fixed point theorem for Suzuki type (alpha, r)-admissible contractions.
Citation - WoS: 5
Citation - Scopus: 7
Irremissible Stimulate on 'unified Fixed Point Theorems in Fuzzy Metric Spaces Via Common Limit Range Property'
(Springeropen, 2014) Roldan-Lopez-de-Hierro, Antonio-Francisco; Karapinar, Erdal; Kumam, Poom; Mathematics
One of the goals of this short note is to alert researchers as regards some mistakes that appeared in a recent paper (Chauhan, Khan and Kumar in J. Inequal. Appl. 2013: 182, 2013). This entails main proofs based on a false result, which invalidates all statements. We also give a complete revision of the antecedents of this work in order to find the main reasons of the mistakes. Finally, the main aim of this note is to propose a correct, more general version of the main theorems in the paper mentioned.
Citation - WoS: 14
Citation - Scopus: 12
Matkowski Theorems in the Context of Quasi-Metric Spaces and Consequences on g-metric Spaces
(Sciendo, 2016) Karapinar, Erdal; Roldan-Lopez-de-Hierro, Antonio-Francisco; Samet, Bessem; Mathematics
In this paper, we prove the characterization of a Matkowski's theorem in the setting of quasi-metric spaces. As a result, we observe that some recent fixed point results in the context of G-metric spaces are consequences of our main result.
Citation - WoS: 4
Citation - Scopus: 4
A Note on '(g, f)-closed Set and Tripled Point of Coincidence Theorems for Generalized Compatibility in Partially Metric Spaces'
(Springeropen, 2014) Karapinar, Erdal; Roldan-Lopez-de-Hierro, Antonio-Francisco; Mathematics
Recently, some (common) multidimensional fixed theorems in partially ordered complete metric spaces have appeared as a generalization of existing (usual) fixed point results. Unexpectedly, we realized that most of such (common) coupled fixed theorems are either weaker or equivalent to existing fixed point results in the literature. In particular, we prove that the results included in the very recent paper (Charoensawan and Thangthong in Fixed Point Theory Appl. 2014:245, 2014) can be considered as a consequence of existing fixed point theorems on the topic in the literature.
Citation - WoS: 1
Citation - Scopus: 2
On an Extension of Contractivity Conditions Via Auxiliary Functions
(Springer international Publishing Ag, 2015) Agarwal, Ravi P.; Karapinar, Erdal; Roldan-Lopez-de-Hierro, Antonio-Francisco; Mathematics
In this manuscript, we study sufficient conditions on the functions that appears in very complex contractivity conditions introduced in a recent manuscript by Liu et al. in order to guarantee the existence and uniqueness of common fixed points of four self-mappings.
Citation - WoS: 11
Citation - Scopus: 19
On Some Fixed Point Theorems Under (α, Ψ, Φ)-Contractivity Conditions in Metric Spaces Endowed With Transitive Binary Relations
(Springer international Publishing Ag, 2015) Shahzad, Naseer; Karapinar, Erdal; Roldan-Lopez-de-Hierro, Antonio-Francisco; Mathematics
After 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.
Citation - WoS: 57
Citation - Scopus: 62
A Proposal to the Study of Contractions in Quasi-Metric Spaces
(Hindawi Ltd, 2014) Alsulami, Hamed H.; Karapinar, Erdal; Khojasteh, Farshid; Roldan-Lopez-de-Hierro, Antonio-Francisco; Mathematics
We investigate the existence and uniqueness of a fixed point of an operator via simultaneous functions in the setting of complete quasi-metric spaces. Our results generalize and improve several recent results in literature.
Citation - WoS: 24
Citation - Scopus: 5
Remarks on 'Coupled coincidence point results for a generalized compatible pair with applications'
(Springer international Publishing Ag, 2014) Erhan, Inci M.; Karapinar, Erdal; Roldan-Lopez-de-Hierro, Antonio-Francisco; Shahzad, Naseer; Mathematics
Very 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.
Citation - WoS: 3
Citation - Scopus: 4
A Short-Note on 'common Fixed Point Theorems for Non-Compatible Self-Maps in Generalized Metric Spaces'
(Springer international Publishing Ag, 2015) Roldan-Lopez-de-Hierro, Antonio-Francisco; Karapinar, Erdal; Alsulami, Hamed H.; Mathematics
The main aim of this short-note is point out that certain hypotheses assumed on some results in the very recent paper (Yang in J. Inequal. Appl. 2014:275, 2014) are unnecessary, and the results contained in that manuscript can easily be improved.
Citation - WoS: 10
Citation - Scopus: 9
Some Inevitable Remarks on "tripled Fixed Point Theorems for Mixed Monotone Kannan Type Contractive Mappings"
(Hindawi Publishing Corp, 2014) Alsulami, Hamed H.; Roldan-Lopez-de-Hierro, Antonio-Francisco; Karapinar, Erdal; Radenovic, Stojan; Mathematics
We advise that the proof of Theorem 12 given by Borcut et al. (2014) is not correct, and it cannot be corrected using the same technique. Furthermore, we present some similar results as an approximation to the opened question if that statement is valid.
Citation - WoS: 41
Citation - Scopus: 44
Some New Fixed Point Theorems in Fuzzy Metric Spaces
(Ios Press, 2014) Roldan-Lopez-de-Hierro, Antonio-Francisco; Karapinar, Erdal; Manro, Saurabh; Mathematics
The aim of this paper is to introduce a new class of contractive mappings such as fuzzy alpha-psi-contractive mappings and to present some fixed point theorems for such mappings in complete fuzzy metric space in the sense of Kramosil and Michalek. The results presented in this paper substantially generalize and extend several comparable results in the existing literature. Also, some examples are given to support the usability of our results.
Citation - Scopus: 1
Some Remarks About the Existence of Coupled g-coincidence Points
(Springeropen, 2015) Erhan, Inci M.; Roldan-Lopez-de-Hierro, Antonio-Francisco; Shahzad, Naseer; Mathematics
Very 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.
Citation - WoS: 5
Citation - Scopus: 4
Some remarks on 'Multidimensional fixed point theorems for isotone mappings in partially ordered metric spaces'
(Springer international Publishing Ag, 2014) Agarwal, Ravi P.; Karapinar, Erdal; Roldan-Lopez-de-Hierro, Antonio-Francisco; Mathematics
The main aim of this paper is to advise researchers in the field of Fixed Point Theory against an extended mistake that can be found in some proofs. We illustrate our claim proving that theorems in the very recent paper (Wang in Fixed Point Theory Appl. 2014: 137, 2014) are incorrect, and we provide different corrected versions of them.