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Article Citation - WoS: 9Citation - Scopus: 8Existence and Uniqueness of Best Proximity Points Under Rational Contractivity Conditions(Walter de Gruyter Gmbh, 2016) Karapinar, Erdal; Roldan-Lopez-de-Hierro, Antonio-Francisco; Sadarangani, KishinThe 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.Article Citation - WoS: 41Citation - Scopus: 44Some New Fixed Point Theorems in Fuzzy Metric Spaces(Ios Press, 2014) Roldan-Lopez-de-Hierro, Antonio-Francisco; Karapinar, Erdal; Manro, SaurabhThe 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.Article Citation - WoS: 1DISCUSSION ON THE EQUIVALENCE OF W-DISTANCES WITH Ω-DISTANCES(Yokohama Publ, 2015) Roldan-Lopez-de-Hierro, Antonio-Francisco; Karapinar, ErdalIn 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.Article Citation - WoS: 171Citation - Scopus: 189Coincidence 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, JuanDue 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.
