(b) Show that if X is uniformly convex and (xn) ⊂ X such that lim n→∞ ‖xn‖ = 1 and lim n,m→∞ ‖xn + xm‖ = 2, then (xn) is convergent. Proceed as follows. Use the definition to prove first that if all terms in the sequence have unit length, then the sequence is Cauchy. In the general case, let yn = xn/‖xn‖. Prove that lim n,m→∞ ‖yn + ym‖ = 2. Then, combine this with what you have shown already to prove that (xn) must be Cauchy. (c) Prove that if X is uniformly convex and S ⊂ X is closed and convex, then S contains a unique element of minimal norm, that is, a unique s0 ∈ S such that inf s∈S ‖s‖ = ‖s0‖. Proceed as follows. Let d = inf s∈S ‖s‖. Now, use part (b) to construct a

On Uniformly Convex Spaces

Let @l denote any one of the classical spaces @?"~, c, c"0 and @?"p of bounded, convergent, null and absolutely p-summable sequences, respectively, and @l@^ also be the domain of the generalized difference matrix B(r,s) in the sequence space @l, where 1@?p<~. The present paper is devoted to studying on the sequence space @l@^. Furthermore, the @b- and @c-duals of the space @l@^ are determined, and the Schauder bases for the spaces c@^, c@^"0 and @?@^"p are given, and some topological properties of the spaces c@^"0, @?@^"1 and @?@^"p are examined. Finally, the classes (@l@^"1:@l"2) and (@l@^"1:@l@^"2) of infinite matrices are characterized, where @l"1@?{@?"~,c,c"0,@?"p,@?"1} and @l"2@?{@?"~,c,c"0,@?"1}.

Some new sequence spaces derived by the domain of generalized difference matrix

Graphical abstractDisplay Omitted HighlightsThe proposed method is applied on UCI Machine Learning Repository datasets and its corresponding performance measures are obtained.The comparison of the proposed similarity measures with the existing results reveal that the accuracy obtained by the present technique provides better similarity rating.It is also observed that fixing the threshold values for the similarity measures is difficult due to the negative rating in some existing methodology.The above difficulty can be avoided by using this newly proposed technique, in which the similarity measures lies between 0 and 1.The similarity rating obtained by the suggested technique is compared with the class distribution data set and are analyzed.The proposed method exhibits more accuracy, sensitivity, ROC curves, AUC values and enhanced F-measure than the existing methods. In this paper, a new similarity measure and a weighted similarity measure on intuitionistic fuzzy soft sets (IFSSs) are proposed and some of their basic properties are discussed. Using the proposed similarity measure, a relation (?α) between two IFSSs are defined and it is found that the defined relation is not an equivalence relation. Further, the effectiveness of the proposed similarity measure is demonstrated in a numerical example with the help of measure of performance and measure of error. Moreover, medical diagnosis problems have been exhibited through a hypothetical case study by using this proposed similarity measure. Finally, the proposed method is applied to 10 different medical data sets from UCI Machine Learning Repository datasets and its similarity measures are calculated. The corresponding performance measures, like, accuracy, sensitivity, specificity, ROC curves, AUC values, and F-measures are obtained and it is compared with the existing methods. This shows that the proposed method exhibits more accuracy, sensitivity and enhanced F-measures than the existing methods.

A similarity measure of intuitionistic fuzzy soft sets and its application in medical diagnosis

Some i-convergent sequence spaces dened by orlicz functions

The venerable math programs Maple and Mathematica long ago outgrew pure math to include numerical and symbolic math, graphics, document preparation, and more. Maplesoft and Wolfram have each recently released a major update-Maple 12 and Mathematica 7-and Maple has a new simulation package as well. The company is increasingly pitching to engineers-an approach that has long been successful for another big math program, MathWorks' Matlab.

http://ieeexplore.ieee.org/iel5/6/4808366/04808380.pdf

New math

In this paper, we introduce the concepts of pointwise and uniform statistical convergence of order α for sequences of real-valued functions. Furthermore, we give the concept of an α-statistically Cauchy sequence for sequences of real-valued functions and prove that it is equivalent to pointwise statistical convergence of order α for sequences of real-valued functions. Also, some relations between S α (f )-statistical convergence and strong w β p (f )-summability are given. MSC: 40A05; 40C05; 46A45

/pdf/on-pointwise-and-uniform-statistical-convergence-of-order-a-49ssp1oaad.pdf

On pointwise and uniform statistical convergence of order α for sequences of functions

Generalized difference sequence spaces and their dual spaces

In this paper we define the sequence space lM (Δm, p, q, s) on a seminormed complex linear space by using an Orlicz function. We study its different algebraic and topological properties like solidness, symmetricity, monotonicity, convergence free etc. We prove some inclusion relations involving lM (Δm, p, q, s).

Generalized difference sequence spaces on seminormed space defined by Orlicz functions

In this paper we introduce some generalized difference sequence spaces and investigate inclusion relations and Kothe-Toeplitz duals.

On Some New Generalized Difference Sequence Spaces

In this study we introduce the concept of S α (f )-statistical convergence of sequences of real valued functions. Also some relations between S α (f )-statistical convergence and strong w βp (f )-summability are given. MSC: 40A05; 40C05; 46A45

https://link.springer.com/content/pdf/10.1186%2F1029-242X-2013-204.pdf

Mikail Et

Papers

On pointwise and uniform statistical convergence of order α for sequences of functions

Generalized difference sequence spaces and their dual spaces

Generalized difference sequence spaces on seminormed space defined by Orlicz functions

On Some New Generalized Difference Sequence Spaces

On λ-statistical convergence of order α of sequences of function