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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, 121–142, 1997).Article A COUPLED FIXED POINT RESULT IN PARTIALLY ORDERED PARTIAL METRIC SPACES THROUGH IMPLICIT FUNCTION(Hacettepe Univ, FAC Sci, 2013) Özyurt, Selma Gülyaz; Karapınar, Erdal; Gulyaz, SelmaIn 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
