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Article Citation - WoS: 17Citation - Scopus: 27Fixed Point Theorems in New Generalized Metric Spaces(Springer Basel Ag, 2016) Karapinar, Erdal; Karapınar, Erdal; O'Regan, Donal; Roldan Lopez de Hierro, Antonio Francisco; Shahzad, Naseer; Karapınar, Erdal; Mathematics; MathematicsThe aim of our paper is to present new fixed point theorems under very general contractive conditions in generalized metric spaces which were recently introduced by Jleli and Samet in [Fixed Point Theory Appl. 2015 (2015), doi:10.1186/s13663-015-0312-7]. Although these spaces are not endowed with a triangle inequality, these spaces extend some well known abstract metric spaces (for example, b-metric spaces, Hitzler-Seda metric spaces, modular spaces with the Fatou property, etc.). We handle several types of contractive conditions. The main theorems we present involve a reflexive and transitive binary relation that is not necessarily a partial order. We give a counterexample to a recent fixed point result of Jleli and Samet. Our results extend and unify recent results in the context of partially ordered abstract metric spaces.Article Citation - Scopus: 1Discussion on the Equivalence of W-Distances With Ω-Distances(Yokohama Publications, 2015) Roldán-López-De-Hierro,A.-F.; Karapınar, Erdal; Karapinar,E.; Karapınar, Erdal; Mathematics; MathematicsIn this manuscript, we study some relationships between w-distances on metric spaces and Ω-distances on G*-metric spaces. Concretely we show that the class of all w-distances on metric spaces is a subclass of all Ω-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 Ω-distances. In this sense, we show how to translate some results between different metric models. © 2015.Article Citation - WoS: 33Citation - Scopus: 34Iterative Approximation of Fixed Points for Presic Type f-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 On Pairs of $ell$-Köthe Spaces(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, 121–142, 1997).Article A COUPLED FIXED POINT RESULT IN PARTIALLY ORDERED PARTIAL METRIC SPACES THROUGH IMPLICIT FUNCTION(2013) Özyurt, Selma Gülyaz; Karapınar, ErdalIn this manuscript, we discuss the existence of coupled fixed points inthe context of partially ordered metric spaces through implicit relationsfor mappings F : X× X -> X such that F has the mixed monotoneproperty. Our main theorem improves and extends various results inthe literature. We also state an example to illustrate our work
