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Article Citation - WoS: 15Contractive Multivalued Maps in Terms of q-functions on Complete Quasimetric Spaces(Springer international Publishing Ag, 2014) Karapinar, Erdal; Romaguera, Salvador; Tirado, PedroIn this paper we prove the existence of a fixed point for multivalued maps satisfying a contraction condition in terms of Q-functions, and via Bianchini-Grandolfi gauge functions, for complete T-0-quasipseudometric spaces. Our results extend, improve, and generalize some recent results in the literature. We present some examples to validate and illustrate our results.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: 10Fixed Point Results in Orbitally Complete Partial Metric Spaces(Malaysian Mathematical Sciences Soc, 2013) Nashine, Hemant Kumar; Karapinar, ErdalIn this paper, we prove two fixed point theorems for maps that satisfy a contraction principle involving a rational expression in complete partial metric spaces.Article Citation - WoS: 35Citation - Scopus: 46Some unique fixed point theorems for rational contractions in partially ordered metric spaces(Springeropen, 2013) Arshad, Muhammad; Karapinar, Erdal; Ahmad, JamshaidIn this paper, we prove some unique fixed point results for an operator T satisfying certain rational contraction condition in a partially ordered metric space. Our results generalize the main result of Jaggi (Indian J. Pure Appl. Math. 8(2):223-230, 1977). We give several examples to show that our results are proper generalization of the existing one. MSC: 47H10, 54H25, 46J10, 46J15.Article Citation - WoS: 21Citation - Scopus: 23Best Proximity Points of Generalized Almost Ψ-Geraghty Contractive Non-Self(Springer international Publishing Ag, 2014) Aydi, Hassen; Karapinar, Erdal; Erhan, Inci M.; Salimi, PeymanIn this paper, we introduce the new notion of almost psi-Geraghty contractive mappings and investigate the existence of a best proximity point for such mappings in complete metric spaces via the weak P-property. We provide an example to validate our best proximity point theorem. The obtained results extend, generalize, and complement some known fixed and best proximity point results from the literature.Article Citation - WoS: 4Citation - Scopus: 4Fixed Point Theorems for Generalized Weak Contractions Satisfying Rational Expression on a Ordered Partial Metric Space(Maik Nauka/interperiodica/springer, 2013) Karapinar, Erdal; Marudai, M.; Pragadeeswarar, V.The purpose of this manuscript is to present a fixed point theorem using a generalized weak contraction condition of rational type in the context of partial metric spaces.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: 5Citation - Scopus: 14Existence of a Solution of Integral Equations Via Fixed Point Theorem(Springeropen, 2013) Gulyaz, Selma; Karapinar, Erdal; Rakocevic, Vladimir; Salimi, PeymanIn this paper, we establish a solution to the following integral equation: u(t) = integral(T)(0) G(t, s)f(s, u(s)) ds for all t is an element of [0,T], (1) where T > 0, f : [0, T] x R -> R and G : [0, T] x [0, T] -> [0, infinity) are continuous functions. For this purpose, we also obtain some auxiliary fixed point results which generalize, improve and unify some fixed point theorems in the literature.Article Citation - WoS: 77Citation - Scopus: 81α-admissible mappings and related fixed point theorems(Springeropen, 2013) Hussain, Nawab; Karapinar, Erdal; Salimi, Peyman; Akbar, FarhanaIn this paper, we prove the existence and uniqueness of a fixed point for certain alpha-admissible contraction mappings. Our results generalize and extend some well-known results on the topic in the literature. We consider some examples to illustrate the usability of our results.Article Citation - WoS: 14Citation - Scopus: 24Generalized Alpha-Psi Type Mappings of Integral Type and Related Fixed Point Theorems(Springer, 2014) Karapinar, Erdal; Shahi, Priya; Tas, KenanThe aim of this paper is to introduce two classes of generalized alpha-psi-contractive type mappings of integral type and to analyze the existence of fixed points for these mappings in complete metric spaces. Our results are improved versions of a multitude of relevant fixed point theorems of the existing literature.
