On cesaro summable sequences of continuous functions pdf

Cesaro summability implies bounded partial sums physics. Many important sequence spaces arise in a natural way. We now introduce a sequence space c, cesaro summable difference. Note that each of the sets fak j n kg that appears in. C, 1 summability in chapter i we saw that the notion of pointwise convergence is not the ideal one in dealing with fourier series of summable functions.

The set of all sequences series that are summable by a given method is called the summability field of the given method. Now divide the sum on the right hand side into two parts. Cesaro summable sequence spaces over the nonnewtonian. Also fuzzy realvalued cesaro summable triple sequence space is introduced. In order that the limit of a convergent sequence of continuous functions be a continuous function, it is sufficient, but not necessary, that the convergence be uniform. Some new type of lacunary difference sequence spaces defined by sequence of orlicz functions. As a function of q, this is the riemann zeta function. Assam, india 2,3department of mathematics, national institute of technology, silchar. A new class of sequences related to the spaces defined by. On cesaro summable sequences of continuous functions volume 42 issue 1 sophocles mercourakis. Searching for just a few words should be enough to get started. Now this is nonsense unless we use a different definition of sum convergence, such as the cesaro summation. Some new classes of statistical convergent fuzzy real. Lecture 15 we have seen that a sequence of continuous functions.

We also study some topological properties and inclusion rela. A new type of convergence called uniformly pointwise conver gence for a sequence of scalar valued functions is introduced. Pdf strongly cesaro type quasicauchy sequences researchgate. Etlacunary statistical convergence and strongly lacunary summable functions of. Indeed square summable sequences form a vector space. The stolzcesaro theorem has numerous applications in calculus. On a convolution of sequences ln a compact group by gilbert helmberg communicated by prof. How can we show that the bounded sequences which are cesaro summable, i.

In the present paper we introduce some strongly convergent di. Then and are summable, and if is not summable, and, then is not summable. On cesaro summable sequences of continuous functions. We say that fn converges pointwise to a function f on e for each x. A summability method s is called an rtype summability method if 5 is regular and xy is strongly 5 summable to 0 whenever x is strongly 5 summable to 0 and y is a bounded sequence.

Get started when the numbers on these plates are arranged in order, the differences. The point of this theorem is that a sequence only has values for each positive integer. Statistically convergent and cesaro summable fuzzy real. If you need to make more complex queries, use the tips below to guide you. Spaces of cesaro difference sequences of order r defined by a modulus function in a. Note that if the sequence an l, then it is c,1summable to the sum l. Suppose a n fn for some function fx and that lim x. A similar integral test would show that the series converges when q 1, while it diverges when q. Wealsoprovethatifafunction is uniformly continuous on a subset of r,then, is quasicauchy whenever is a quasicauchy sequence of points in.

Convergence of a sequence of bounded continuous functions on x with re. P relate linear functions and arithmetic sequences, then solve problems related to arithmetic sequences. Homework equations the attempt at a solution i tried contraposition. We can add two square summable sequences to get another such. On various new concepts of statistical convergence for. Chapter 8 sequences and series of functions given a set a, a sequence of elements of a is a function f. Some new type of lacunary difference sequence spaces. In this paper, we introduce the concepts of pointwise and uniform statistical convergence of order. On pointwise and uniform statistical convergence of order. E, the sequence of real numbers fnx converges to the number fx. Some algebraic and topological properties such as solid, monotone, symmetric, convergence free, sequence algebra etc. A sequence aa n of complex numbers or more generally, elements of a banach space is called summable if nsup x n2e ja nj. Stronglysummable sequences defined by orlicz functions.

It is clear that the limit superior of fakg exists if the sequence is not bounded above, so assume that there is an upper bound m for the sequence. In this paper, following a very recent and new approach of aizpuru et al. Determine all complexvalued functions f, which are continuous in 0,2. The corrected version of this theorem is given here. Some strongly convergent difference sequence spaces defined by a sequence of modulus functions kuldip raj1 and sunil k. The pnorm can be extended to vectors that have an infinite number of components, which yields the space. The product of two summable sequences is not necessarily summable.