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Yayın Lacunary d-Statistical Boundedness of Order ? in Metric Spaces(Inst Math & Mechanics Azerbaijan, 2022) Kandemir, H. S.; Et, M.; Cakalli, H.Daha fazla In this study, using a lacunary sequence we introduce the concepts of lacunary d-statistically convergent sequences of order alpha and lacunary d-statistically bounded sequences of order alpha in general metric spaces.Daha fazla Yayın A quest of G-continuity in neutrosophic spaces(Wiley, 2021) Açıkgöz, Ahu; Cakalli, H.; Esenbel, Ferhat; Kocinac, Ljubisa D. R.Daha fazla Continuity, in particular sequential continuity, is an important subject of investigation not only in topology but also in some other branches of mathematics. Connor and Grosse-Erdmann remodelled its definition for real functions by replacing lim with an arbitrary linear functional G defined on a linear subspace of the vector space of all real sequences. Then, this definition was extended to a topological group X by replacing a linear functional G with an arbitrary additive function defined on a subgroup of the group of all X-valued sequences. Also, some new theorems in generalized setting were given, and some other theorems that had not been obtained for real functions were presented. In this study, we introduce neutrosophic G-continuity and investigate its properties in neutrosophic topological spaces.Daha fazla Yayın Sequential definitions of compactness(PERGAMON-ELSEVIER SCIENCE LTD, 2008) Cakalli, H.Daha fazla A subset F of a topological space is sequentially compact if any sequence x = (x(n)) of points in F has a convergent subsequence whose limit is in F. We say that a subset F of a topological group X is G-sequentially compact if any sequence x = (x(n)) of points in F has a convergent subsequence y such that G(y) is an element of F where G is an additive function from a subgroup of the group of all sequences of points in X. We investigate the impact of changing the definition of convergence of sequences on the structure of sequentially compactness of sets in the sense of G-sequential compactness. Sequential compactness is a special case of this generalization when G = lim. (C) 2007 Elsevier Ltd. All rights reserved.Daha fazla Yayın STATISTICAL CONVERGENCE OF DOUBLE SEQUENCES IN TOPOLOGICAL GROUPS(EUDOXUS PRESS, LLC, 2010) Cakalli, H.; Savas, E.Daha fazla The idea of statistical convergence of double sequences was first introduced by Mursaleen and Edeley [12]) while the idea of statistical convergence of single sequences was first studied by Past [7] and the rapid developments were started after the papers of Salat [14] and Fridy [8]. Nowadays it has become one of the most active area of research in the field of summability. In this paper, we give an extension of statistical convergence of double sequences to topological groups and give theorems in this general setting.Daha fazla Yayın Summability in topological spaces(PERGAMON-ELSEVIER SCIENCE LTD, 2011) Cakalli, H.; Khan, M. K.Daha fazla The main purpose of the paper is to introduce the notion of summability in abstract Hausdorff topological spaces. We give a characterization of such summability methods when the space allows a countable base. We also provide several Tauberian theorems in topological structures. Some open problems are discussed. (C) 2010 Elsevier Ltd. All rights reserved.Daha fazla