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Article Citation - WoS: 35Citation - Scopus: 39Metric-Like Spaces To Prove Existence of Solution for Nonlinear Quadratic Integral Equation and Numerical Method To Solve It(Elsevier Science Bv, 2018) Hazarika, Bipan; Karapinar, Erdal; Arab, Reza; Rabbani, MohsenThe purpose of this paper is to obtain some common fixed point results for two mappings satisfying various contractive conditions in metric-like spaces. These results extend some previous results in the literature, since the condition under which the operator admits common fixed points is more general than the others in literature. Therefore, several well known results are generalized. As an application we use these results to existence of solution for nonlinear quadratic integral equation. To credibility, we apply modified homotopy and Adomian decomposition method to find solution of the above problem with high accuracy. (C) 2017 Elsevier B.V. All rights reserved.Article Citation - WoS: 171Citation - Scopus: 191Coincidence 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.Article Citation - WoS: 13Citation - Scopus: 14Coincidence Point Theorems on Quasi-Metric Spaces Via Simulation Functions and Applications To g-metric Spaces(Springer Basel Ag, 2018) Lopez de Hierro, A. F. Roldan; Karapinar, E.; O'Regan, D.In this paper, we present some coincidence point results in the framework of quasi-metric spaces using contractive conditions involving simulation functions. As consequences, we are able to particularize these results to a variety of situations including G-metric spaces. The results presented in this paper generalize and extend several comparable results in the existing literature. In addition, some examples are given.
