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Publication Metadata only New distortion theorems for Sakaguchi functions(ELEMENT, R AUSTRIJE 11, 10000 ZAGREB, CROATIA, 2007-10) Çağlar, Mert; POLATOĞLU, YAŞAR; TR199370; TR108339Let A be the class of functions f (z) of the form f (z) = z + Sigma(infinity)(k=2), a(k)z(k) that are analytic in the open unit disk D = {(z) epsilon C | |z| < 1} in 1959, K. Sakaguchi [9] has considered the subclass of A consisting of those f (z) which satisfy Re (zf,(z)/f(z)-f(-z)) > 0, where z E D. We call such a function a "Sakaguchi function", and denote the class of those functions by Ss. Various authors have studied this class ([6, 7, 9, 10]). We obtain new distortion theorems, Koebe domain, k-quasiconformatity, and the radius of convexity for the class S-s.Publication Metadata only Weakly Compact-Friendly Operators(Institution Of Russian Academy Of Sciences South Mathematical İnstitute Of Vladikavkaz Scientific Center Of The Russian Academy Of Sciences And The Government Of Republic Of North Ossetia-Alania, 22, Markusa Street, Vladikavkaz, 362027, 2009) Çağlar, Mert; Mısırlıoğlu, Remzi Tunç; TR108339; TR108824We introduce weak compact-friendliness as an extension of compact-friendliness, and and prove that if a non-zero weakly compact-friendly operator B: E→ E on a Banach lattice is quasi-nilpotent at some non-zero positive vector, then B has a non-trivial closed invariant ideal. Relevant facts related to compact-friendliness are also discussed.Publication Embargo Multivalued starlike functions of complex order(2008) Çağlar, Mert; Owa, Shigeyoshi; YAVUZ, EMEL; POLATOĞLU, YAŞAR; 199370; 111202Let S ∗ λ (1−b)(b 6= 0, complex) denote the class of functions f(z) = z+a2z 2+· · · analytic in the open unit disc D = {z ∈ CPublication Embargo Lambda-fractional properties of generalized Janowski functions in the unit disc(2008) Çağlar, Mert; YAVUZ, EMEL; POLATOĞLU, YAŞAR; 108339; 108339; 111202For analytic function f(z) = z + a2z 2 + · · · in the open unit disc D, a new fractional operator Dλf(z) is defined. Applying this fractional operator Dλf(z) and the principle of subordination, we give new proofs for some classical results concerning the class S ∗ λ (A, B, α) of functions f(z).Publication Embargo Schwarzian Derivative Revisited(İstanbul Kültür Üniversitesi Yayınları, 2006-12) Çağlar, Mert; Demirer, R. Murat; POLATOĞLU, YAŞAR; TR199370The Boolean-algebraic structure of the so-called Schwarzian derivative is investigated. A sufficient condition for a function of several variables to behave chaotically, which concerns its associated Schwarzian derivative, is also given.Publication Metadata only Coefficient Inequality For Perturbed Harmonic Mappings(Pergamon-Elsevier Science Ltd, The Boulevard, Langford Lane, Kidlington, Oxford Ox5 1Gb, England, 2010-08) Çağlar, Mert; Yavuz Duman, Emel; POLATOĞLU, YAŞAR; TR199370; TR108339; TR111202The aim of this work is to give the coefficient inequality for the perturbed harmonic mappings in the open unit disc D. (c) 2010 Elsevier Ltd. All rights reserved.Publication Metadata only Invariant subspaces for positive operators on locally convex solid Riesz spaces(ELSEVIER SCIENCE BV, PO BOX 211, 1000 AE AMSTERDAM, NETHERLANDS, 2007-09-24) Zafer, Ercan; Çağlar, Mert; TR108339; TR181147We prove that an x(0)-quasinilpotent semigroup S of continuous positive linear operators on a locally convex solid Riesz space X has a common invariant subspace. Using this, a result which implies the main theorem of Abramovich, Aliprantis and Burkinshaw [J. Funct. Anal. 115 (1993) 418-424] is also given.Publication Embargo On Janowski starlike functions(Springer International Publishing Ag, Gewerbestrasse 11, Cham, Ch-6330, Switzerland, 2007) Çağlar, Mert; Şen, A.; Owa, Shigeyoshi; YAVUZ, EMEL; POLATOĞLU, YAŞAR; 108339; 199370; 111202For analytic functions f(z) in the open unit disc U with f(0) = 0 and f'(0) = 1, applying the fractional calculus for f(z), a new fractional operator D-lambda f(z) is introduced. Further, a new subclass F-lambda(*)(A, B) consisting of f(z) associated with Janowski function is defined. The objective of the present paper is to discuss some interesting properties of the class F-lambda(*)(A, B). Copyright (c) 2007.Publication Metadata only Positive Operators on Hilbert Lattices(International Conference on Theory and Applications of Mathematics and Informatics, ICTAMI, 2009) Mısırlıoğlu, Remzi Tunç; Çağlar, Mert; Çavuşoğlu, Özlem; ÇAĞLAR, MERT; 108824; 108339Publication Embargo Inequalities for the Schwarzian derivative for subclasses of convex functions in the unit disc(2006) Çağlar, Mert; Şen, Arzu; POLATOĞLU, YAŞAR; 108339; 199370Nehari norm of the Schwarzian derivative of an analytic function is closely related to its univalence. The famous NehariKraus theorem ((3), (4)) and AhlforsW eill theorem (1) are of fundamental importance in this direction. For a non-constant meromorphic function f on D the unite disc, the Schwarzian derivative Sf of f by is holomorphic at z02 D if and only if f is locally univalent at z0. The aim of this paper is to give sharp estimates of the Nehari norm for the subclasses of convex functions in the unit disc.
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