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https://hdl.handle.net/11467/77

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λ-statistical convergence in n-normed spaces
(2013) Hazarika, Bipan; Savaş, Ekrem
In this paper, we introduce the concept of ?-statistical convergence in n-normed spaces. Some inclusion relations between the sets of statistically convergent and ?-statistically convergent sequences are established. We find its relations to statistical convergence, (C,1)-summability and strong (V, ?)-summability in n-normed spaces.
On ii>θ -statistical convergence of order α in intuitionistic fuzzy normed spaces
(Editura Acad Romane, 2015) Savaş, Ekrem
In this paper, following a very recent and new approach, we introduce the notions of I -statistical convergence and I-theta -statistical convergence of order alpha, where 0 < alpha <= 1, with respect to the intuitionistic fuzzy norm (mu,nu) and we mainly investigate their relationship, and also make some observations about these classes.
On asymptotically lacunary σ-statistical equivalent sequences of fuzzy numbers
(World Scientific Publ Co Pte Ltd, 2009) Savaş, Ekrem
This paper presents the asymptotically lacunary sigma-statistical equivalent which is a natural combination of the definition for asymptotically equivalent, invariant mean and lacunary statistical convergence of fuzzy numbers. In addition, we shall also present asymptotically lacunary sigma-statistical equivalent analogs of Savas and Nuray's theorems in Ref. 8.
Generalized statistical convergence and statistical core of double sequences
(Springer Heidelberg, 2010) Mursaleen, Mohammad; Çakan, Celal; Mohiuddine, Syed Abdul; Savaş, Ekrem
In this paper we extend the notion of lambda-statistical convergence to the (lambda, A mu)statistical convergence for double sequences x = (x (jk) ). We also determine some matrix transformations and establish some core theorems related to our new space of double sequences S (lambda,A mu).
Measurement of K-shell absorption jump factors and jump ratios in some lanthanide elements using EDXRF technique
(Pergamon-Elsevier Science Ltd, 2013) Polat, Recep; İçelli, Orhan; Yalçın, Zeynel; Pesen, Erhan; Orak, Salim
59.5 keV gamma rays scattered by an aluminum foil have been used as a radiation source to measure the absorption jump factor and jump ratios for absorbers Ce, Pr, Nd, Sm, Eu and Tb. The theoretical and experimental values are compared with the corresponding ones in the literature.
(A)Δ - double sequence spaces of Fuzzy numbers via orlicz function
(Univ Sistan & Baluchestan, 2011) Savaş, Ekrem
The aim of this paper is to introduce and study a new concept of strong double (A)(Delta)-convergent sequence of fuzzy numbers with respect to an Orlicz function and also some properties of the resulting sequence spaces of fuzzy numbers are examined. In addition, we define the double (A, Delta)-statistical convergence of fuzzy numbers and establish some connections between the spaces of strong double (A)(Delta)-convergent sequence and double (A, Delta)-statistical convergent sequence.
Asymptotic equivalence of double sequences
(2012) Patterson, Richard F.; Savaş, Ekrem
The goal of this paper is to present a four-dimensional matrix characterization of asymptotic equivalence of double sequences. This will be accomplished with the following notion of asymptotic equivalence of double sequences. Two double sequences are asymptotic equivalent if and only if P − limk,l xk,l yk,l = 1, where x and y are selected judicially. Using this notion necessary and sufficient conditions on the entries of a four-dimensional matrix are given to ensure that the transformation will preserve asymptotic equivalence.
Remark on double lacunary statistical convergence of fuzzy numbers
(Eudoxus Press, LLC., 2009) Savaş, Ekrem
Y. Altin proved the inclusion relations between the sets of the double statistically convergent and double lacunary statistically convergent sequences of fuzzy numbers. In this paper we show that Altin's condition is suffcient as well as necessary.
On ii>θ -statistical convergence of order α in intuitionistic fuzzy normed spaces
(Editura Acad Romane, 2015) Savaş, Ekrem
In this paper, following a very recent and new approach, we introduce the notions of I -statistical convergence and I-theta -statistical convergence of order alpha, where 0 < alpha <= 1, with respect to the intuitionistic fuzzy norm (mu,nu) and we mainly investigate their relationship, and also make some observations about these classes.
Neutrosophic metric spaces
(Springer, 2020) Kirişçi, Murat; Şimşek, Necip
Neutrosophy consists of neutrosophic logic, probability, and sets. Actually, the neutrosophic set is a generalisation of classical sets, fuzzy set, intuitionistic fuzzy set, etc. A neutrosophic set is a mathematical notion serving issues containing inconsistent, indeterminate, and imprecise data. The notion of intuitionistic fuzzy metric space is useful in modelling some phenomena where it is necessary to study the relationship between two probability functions. In this paper, the definition of new metric space with neutrosophic numbers is given. Neutrosophic metric space uses the idea of continuous triangular norms and continuous triangular conorms in intuitionistic fuzzy metric space. Triangular norms are used to generalize with the probability distribution of triangle inequality in metric space conditions. Triangular conorms are known as dual operations of triangular norms. Triangular norms and triangular conorm are very significant for fuzzy operations. Neutrosophic metric space was defined with continuous triangular norms and continuous triangular conorms. Several topological and structural properties neutrosophic metric space have been investigated. The analogues of Baire Category Theorem and Uniform Convergence Theorem are given for Neutrosophic metric spaces.
Finding the traveling wave solutions of some nonlinear partial differential equations by an expansion method
(İstanbul Ticaret Üniversitesi, 2016) Kaya, Doğan
In this study, we construct an expansion method. We have implement this method for finding traveling wave solutions of nonlinear Klein-Gordon equation, Benjamin-Bona-Mahony equation, sixth-order Boussinesq equation and Konopelchenko-Dubrovky system.
Traveling wave solutions of some nonlinear partial differential equations by using extended - expansion method
(İstanbul Ticaret Üniversitesi, 2015) Yokuş, Asıf; Kaya, Doğan
In this study, we use extended (G’/G)-expansion method which is suggested in (Wang et al., 2008). By this method, we find traveling wave solutions of nonlinear Burgers and KdV equations. It is obtained graphics of these solutions by using Mathematica.
A note on |A|(K) summability factors for infinite series
(Springer, 2007) Savaş, Ekrem
We obtain sufficient conditions on a nonnegative lower triangular matrix A and a sequence lambda(n) for the series Sigma a(n)lambda(n)/na(nn) to be absolutely summable of order k >= 1 by A. Copyright (c) 2007 E. Savas, and B. E. Rhoades.
On general summability factor theorems
(Springer International Publishing AG, 2007) Savaş, Ekrem
The goal of this paper is to obtain sufficient and (different) necessary conditions for a series Sigma a(n), which is absolutely summable of order k by a triangular matrix method A, 1 < k <= s < infinity, to be such that Sigma a(n)lambda(n) is absolutely summable of order s by a triangular matrix method B. As corollaries, we obtain two inclusion theorems.
On (Lambda) over-bar-statistically convergent double sequences of fuzzy numbers
(Springer International Publishing AG, 2008) Savaş, Ekrem
We study the notion of (lambda) over bar -statistically convergent for double sequence of fuzzy numbers and also get some inclusion relations. Copyright (C) 2008 Ekrem Savas.
On the cesaro summability of double series
(Springer International Publishing AG, 2008) Savaş, Ekrem; Şevli, Hamdullah; Rhoades, B. E.
In a recent paper by Savas, and Sevli (2007), it was shown that each Cesaro matrix of order alpha, for alpha > -1, is absolutely kth power conservative for k >= 1. In this paper we extend this result to double Cesaro matrices. Copyright (C) 2008.
On absolute cesaro summability
(Springer International Publishing AG, 2009) Şevli, Hamdullah; Savaş, Ekrem
Denote by A(k) the sequence space defined by A(k) = {(s(n)) : Sigma(infinity)(n=1) n(k-1)vertical bar a(n)vertical bar(k) < infinity, a(n) = s(n) - s(n-1)} for k >= 1. In a recent paper by E. Savas, and H. Sevli (2007), they proved every Cesaro matrix of order alpha, for alpha > - 1, (C, alpha) is an element of B(A(k)) for k >= 1. In this paper, we consider a further extension of absolute Cesaro summability. Copyright (C) 2009 H. Sevli and E. Savas.
Summability of double independent random variables
(Hindawi Publishing Corporation, 2008) Patterson, Richard F.; Savaş, Ekrem
We will examine double sequence to double sequence transformation of independent identically distribution random variables with respect to four-dimensional summability matrix methods. The main goal of this paper is the presentation of the following theorem. If max(k,l)vertical bar a(m,n,k,l) vertical bar = max(k,l)vertical bar a(m,k)a(n,l)vertical bar = O(m(-gamma 1))O(n(-gamma 2)) gamma(1),gamma(2) > 0, then E vertical bar X vertical bar(1+1/gamma 1) < infinity and E vertical bar X vertical bar(1+1/gamma 2) < infinity imply that Y(m,n) -> mu almost sure P- convergence.
On double statistical p-convergence of fuzzy numbers
(Springer International Publishing AG, 2009) Savaş, Ekrem; Patterson, Richard F.
Savas and Mursaleen defined the notions of statistically convergent and statistically Cauchy for double sequences of fuzzy numbers. In this paper, we continue the study of statistical convergence by proving some theorems. Copyright (C) 2009 E. Savas, and R. F. Patterson.
A recent note on quasi-power increasing sequence for generalized absolute summability
(Springer, 2009) Savaş, Ekrem; Şevli, Hamdullah
We prove two theorems on vertical bar A,delta vertical bar(k), k >= 1,0 <= delta < 1/k, summability factors for an infinite series by using quasi-power increasing sequences. We obtain sufficient conditions for Sigma a(n)lambda(n) to be summable vertical bar A,delta vertical bar(k), k >= 1, 0 <= delta < 1/k, by using quasi-f-increasing sequences. Copyright (C) 2009 E. Savas, and H. Sevli.

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