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Article Citation - WoS: 172Citation - Scopus: 190Interpolative Reich-Rus Type Contractions on Partial Metric Spaces(Mdpi, 2018) Karapinar, Erdal; Agarwal, Ravi; Aydi, HassenBy giving a counter-example, we point out a gap in the paper by Karapinar (Adv. Theory Nonlinear Anal. Its Appl. 2018, 2, 85-87) where the given fixed point may be not unique and we present the corrected version. We also state the celebrated fixed point theorem of Reich-Rus-Ciric in the framework of complete partial metric spaces, by taking the interpolation theory into account. Some examples are provided where the main result in papers by Reich (Can. Math. Bull. 1971, 14, 121-124; Boll. Unione Mat. Ital. 1972, 4, 26-42 and Boll. Unione Mat. Ital. 1971, 4, 1-11.) is not applicable.Article Citation - WoS: 3Citation - Scopus: 6Some Results on S-contractions of Type e(Mdpi, 2018) Fulga, Andreea; Karapinar, ErdalIn this manuscript, we consider the compositions of simulation functions and E-contraction in the setting of a complete metric space. We investigate the existence and uniqueness of a fixed point for this composite form. We give some illustrative examples and provide an application.Article Citation - WoS: 28Citation - Scopus: 50Non-Unique Fixed Point Results in Extended b-metric Space(Mdpi, 2018) Alqahtani, Badr; Fulga, Andreea; Karapinar, ErdalIn this paper, we investigate the existence of fixed points that are not necessarily unique in the setting of extended b-metric space. We state some examples to illustrate our results.Article Citation - WoS: 35Citation - Scopus: 43A New Approach To the Solution of the Fredholm Integral Equation Via a Fixed Point on Extended b-metric Spaces(Mdpi, 2018) Karapinar, Erdal; Kumari, Panda Sumati; Lateef, DurdanaIt is very well known that real-life applications of fixed point theory are restricted with the transformation of the problem in the form of f(x) = x. (1) The Knaster-Tarski fixed point theorem underlies various approaches of checking the correctness of programs. (2) The Brouwer fixed point theorem is used to prove the existence of Nash equilibria in games. (3) Dlala et al. proposed a solution for magnetic field problems via the fixed point approach. In this paper, by obtaining the fixed point results in an extended b-metric space, we are able to consider real-life applications in a very general frame such as a simple and efficient solution for a Fredholm integral equation by using the technique of a fixed point in the consideration of a new abstract space: the extended b-metric space. Moreover, to address conceptual depth within this approach, we supply illustrative examples of usage where necessary.Article Citation - WoS: 21Citation - Scopus: 27Some Fixed-Point Theorems in b-Dislocated Metric Space and Applications(Mdpi, 2018) Kumari, Panda Sumati; Alqahtani, Obaid; Karapinar, ErdalIn this article, we prove some fixed-point theorems in b-dislocated metric space. Thereafter, we propose a simple and efficient solution for a non-linear integral equation and non-linear fractional differential equations of Caputo type by using the technique of fixed point.Article Citation - WoS: 9Citation - Scopus: 14Sehgal Type Contractions on b-Metric Space(Mdpi, 2018) Alqahtani, Badr; Fulga, Andreea; Karapinar, ErdalIn this paper, we analyze two discontinuous self-mappings that satisfy Sehgal-type inequalities in the setup of complete b-metric space. The main results of the paper cover and extend a few existing results in the corresponding literature. Furthermore, we give some illustrative examples to verify the effectiveness and strength of our derived results. Thereafter, as an application, we consider the obtained result to aggregate the existence and uniqueness of the solution for nonlinear Fredholm integral equations.Article Citation - WoS: 5Citation - Scopus: 7Some Simultaneous Generalizations of Well-Known Fixed Point Theorems and Their Applications To Fixed Point Theory(Mdpi, 2018) Du, Wei-Shih; Karapinar, Erdal; He, ZhenhuaIn this paper, we first establish a new fixed point theorem that generalizes and unifies a number of well-known fixed point results, including the Banach contraction principle, Kannan's fixed point theorem, Chatterjea fixed point theorem, Du-Rassias fixed point theorem and many others. The presented results not only unify and generalize the existing results, but also yield several new fixed point theorems, which are different from the well-known results in the literature.Article Citation - WoS: 140Citation - Scopus: 156On Interpolative Hardy-Rogers Type Contractions(Mdpi, 2019) Karapinar, Erdal; Alqahtani, Obaid; Aydi, HassenBy using an interpolative approach, we recognize the Hardy-Rogers fixed point theorem in the class of metric spaces. The obtained result is supported by some examples. We also give the partial metric case, according to our result.Article Citation - WoS: 34Citation - Scopus: 46Fixed Point Results on -Symmetric Quasi-Metric Space Via Simulation Function With an Application To Ulam Stability(Mdpi, 2018) Alqahtani, Badr; Fulga, Andreea; Karapinar, ErdalIn this paper, in the setting of D - symmetric quasi- metric spaces, the existence and uniqueness of a fixed point of certain operators are scrutinized carefully by using simulation functions. The most interesting side of such operators is that they do not form a contraction. As an application, in the same framework, the Ulam stability of such operators is investigated. We also propose some examples to illustrate our results.
