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Article On Pairs of $ell$-Köthe Spaces(Hacettepe Univ, FAC Sci, 2010) Karapınar, ErdalLet $ell$ be a Banach sequence space with a monotone norm $parallel centerdot parallel_{ell}$, in which the canonical system ($e_i$) is a normalized unconditional basis. Let $a = (a_i), a_i rightarrow infty, lambda=(lambda_i)$ be sequences of positive numbers. We study the problem on isomorphic classification of pairs $F = biggl(K^{ell} biggl( exp biggl(-frac{1}{p}a_i biggr)biggr),K^{ell}biggl(exp biggl(-frac{1}{p}a_i + lambda_i biggr)biggr)biggr)$. For this purpose, we consider the sequence of so-called m-rectangle characteristics $mu^F_m$. It is shown that the system of all these characteristics is a complete quasidiagonal invariant on the class of pairs of finite-type $ell$-power series spaces. By using analytic scale and a modification of some invariants (modified compound invariants) it is proven that m-rectangular characteristics are invariant on the class of such pairs. Deriving the characteristic $tilde{beta}$ from the characteristic $beta$, and using the interpolation method of analytic scale, we are able to generalize some results of Chalov, Dragilev, and Zahariuta (Pair of finite type power series spaces, Note di Mathematica 17, 121&#8211;142, 1997).Article Citation - WoS: 33Citation - Scopus: 34Iterative Approximation of Fixed Points for Presic Type <i>f</I>-contraction Operators(Univ Politehnica Bucharest, Sci Bull, 2016) Abbas, M.; Karapınar, Erdal; Berzig, M.; Nazir, T.; Karapinar, E.; Karapınar, Erdal; Mathematics; Mathematics; MathematicsWe study the convergence of the Presic type k-step iterative process for a class of operators f : X-k -> X satisfying Presic type F-contractive condition in the setting of metric spaces. As an applications of the result presented herein, we derive global attractivity results for a class of matrix difference equations. Numerical experiments are also presented to illustrate the theoretical findings.Article Citation - WoS: 21Citation - Scopus: 20Automatic Continuity of Surjective <i>n</I>-homomorphisms on Banach Algebras(Iranian Mathematical Soc, 2015) Gordji, M. Eshaghi; Jabbari, A.; Karapinar, E.; Eshaghi Gordji, M.; MathematicsIn this paper, we show that every surjective n-homomorphism (n-anti-homomorphism) from a Banach algebra A into a semisimple Banach algebra B is continuous.Article Citation - WoS: 4Citation - Scopus: 4Common Periodic Soft Points of the Asymptotic Sequences in Soft Metric Spaces(Yokohama Publ, 2017) Chen, Chi-Ming; Karapinar, Erdal; MathematicsThe purpose of this paper is to study the important properties of soft sets and soft metric spaces, and then we prove some theorems which assures the existence of common periodic soft points for the asymptotic sequences with respect to the soft Meir-Keeler type functions on a complete soft metric space. Our results generalize many recent fixed point results in the literature.Article Citation - WoS: 5Citation - Scopus: 4Existence and Uniqueness of Common Coupled Fixed Point Results Via Auxiliary Functions(Springer Singapore Pte Ltd, 2014) Chandok, S.; Karapinar, E.; Khan, M. Saeed; Saeed Khan, Mohammad; MathematicsThe purpose of this paper is to establish some coupled coincidence point theorems for mappings having a mixed g-monotone property in partially ordered metric spaces. Also, we present a result on the existence and uniqueness of coupled common fixed points. The results presented in the paper generalize and extend several well-known results in the literature.Article Citation - WoS: 16Citation - Scopus: 19Fixed Point Theorems in Quasi-Metric Spaces and Applications To Multidimensional Fixed Point Theorems on <i>g</I>-metric Spaces(Yokohama Publ, 2015) Agarwal, Ravi; Karapinar, Erdal; Roldan-Lopez-De-Hierro, Antonio-Francisco; MathematicsIn this manuscript, we investigate the equivalence of the coupled fixed point theorems in quasi-metric spaces and in G-metric spaces. We also notice that coupled fixed point theorems in the setting of G-metric spaces can be derived from their corresponding versions in quasi-metric spaces. Our results generalize and unify several fixed point theorems in the context of G-metric spaces in the literature.Article Citation - WoS: 14Citation - Scopus: 11Some Fixed Points Results on Branciari Metric Spaces Via Implicit Functions(North Univ Baia Mare, 2015) Karapinar, Erdal; MathematicsIn this paper, we introduce the notion of alpha-implicit contractive mapping of integral type in the context of Branciari metric spaces. The results of this paper, generalize and improve several results on the topic in literature. We give an example to illustrate our results.Article Citation - WoS: 5Citation - Scopus: 7On Jaggi Type Contraction Mappings(Univ Politehnica Bucharest, Sci Bull, 2018) Karapinar, Erdal; MathematicsBy a work of Jaggi, it is known that the existence of certain inequalities for continuous maps over metric spaces implies the existence and uniqueness of fixed points. In this paper, we show that if p denotes a partial metric, the existence of a rational form of type p(Tt,Ts) <= a(1) p(t,Tt).p(s,Ts)/d(t,s)+a(2)p(t,s) for some a 1 and a 2 with a(1) + a(2) < 1 for a continuous map T over a partial metric space leads to the same conclusions, that is, the existence and uniqueness of fixed points.Conference Object Citation - WoS: 2Citation - Scopus: 2Rational Forms That Imply the Uniqueness of Fixed Points in Partial Metric Spaces(Yokohama Publ, 2019) Karapinar, Erdal; MathematicsIn this paper, we investigate the existence and uniqueness of fixed points of Jaggi type contractions by using a simulation function in the framework of partial metric spaces. Our results improve, extend and unify several results on the topic in the literature.Article Citation - WoS: 19Citation - Scopus: 20Best Proximity Point Theorems for <i>kt</I>-types Cyclic Orbital Contraction Mappings(House Book Science-casa Cartii Stiinta, 2012) Karapinar, Erdal; Petrusel, Gabriela; Tas, Kenan; MathematicsIn this manuscript, three new KT-types cyclic orbital contractions are defined and some related best proximity point theorems are given. Also, the notion of KT-type cyclic orbital Meir-Keeler contraction is defined and some fixed point theorems for this class of mappings are proved. The results of this manuscript generalize some theorems, on the same subject, of several authors, such as Kirk-Srinavasan-Veeramani, Eldered-Veeramani and Karpagam-Agrawal.