In this paper, we introduce and study the system of generalized
vector quasi-variational-like inequalities in Hausdorff topological vector spaces,
which include the system of vector quasi-variational-like inequalities, the
system of vector variational-like inequalities, the system of vector
quasi-variational inequalities, and several other systems as special cases.
Moreover, a number of C-diagonal quasiconvexity properties are proposed for
set-valued maps, which are natural generalizations of the g-diagonal
quasiconvexity for real functions. Together with an application of continuous
selection and fixed-point theorems, these conditions enable us to prove unified
existence results of solutions for the system of generalized vector
quasi-variational-like inequalities. The results of this paper can be seen as
extensions and generalizations of several known results in the
literature.

The system
performance has been analyzed for π/4 DQPSK mapping scheme, which is differential
in nature and hence adding additional advantage. Performance evaluation with
random data as well as some images has been taken. Channel modeling has been
performed in multipath fading environment. For elaboration of the concept
mathematical modeling has been implemented using computer simulation. In this
paper, an attempt is made to know the capabilities of DHT-OFDM with non conventional
mapping technique π/4 DQPSK.

Abstract:
In the present paper, an attempt is made to obtain the degree of approximation of conjugate of functions (signals) belonging to the generalized weighted W(LP, ξ(t)), (p ≥ 1)-class, by using lower triangular matrix operator of conjugate series of its Fourier series.

Abstract:
In the present paper, we define Dislocated Soft Metric Space and discuss about the existence and uniqueness of soft fixed point of a cyclic mapping in soft dislocated metric space. We also prove the unique soft fixed point theorems of a cyclic mapping in the context of dislocated soft metric space. Examples are given for support of the results.

Abstract:
In this article, for a differentiable function , we introduce the definition of the higher-order -invexity. Three duality models for a multiobjective fractional programming problem involving nondifferentiability in terms of support functions have been formulated and usual duality relations have been established under the higher-order -invex assumptions.

Abstract:
Generalization of Szász-Mirakyan operators has been considered by Jain, 1972. Using these generalized operators, we introduce new sequences of positive linear operators which are the integral modification of the Jain operators having weight functions of some Beta basis function. Approximation properties, the rate of convergence, weighted approximation theorem, and better approximation are investigated for these new operators. At the end, we generalize Jain-Beta operator with three parameters , , and and discuss Voronovskaja asymptotic formula. 1. Introduction For ,？？ , let then Equation (1) is a Poisson-type distribution which has been considered by Consul and Jain [1]. In 1970, Jain [2] introduced and studied the following class of positive linear operators: where and has been defined in (1). The parameter may depend on the natural number . It is easy to see that ; (3) reduces to the well-known Szász-Mirakyan operators [3]. Different generalization of Szász-Mirakyan operator and its approximation properties is studied in [4, 5]. Kantorovich-type extension of was given in [6]. Integral version of Jain operators using Beta basis function is introduced by Tarabie [7], which is as follows: In Gupta et al. [8] they considered integral modification of the Szász-Mirakyan operators by considering the weight function of Beta basis functions. Recently, Dubey and Jain [9] considered a parameter in the definition of [8]. Motivated by such types of operators we introduce new sequence of linear operators as follows: For and , where is defined in (1) and The operators defined by (5) are the integral modification of the Jain operators having weight function of some Beta basis function. As special case, the operators (5) reduced to the operators recently studied in [7]. Also, if and , then the operators (5) turn into the operators studied in [8]. In the present paper, we introduce the operators (5) and estimate moments for these operators. Also, we study local approximation theorem, rate of convergence, weighted approximation theorem, and better approximation for the operators . At the end, we propose Stancu-type generalization of (5) and discuss some local approximation properties and asymptotic formula for Stancu-type generalization of Jain-Beta operators. 2. Basic Results Lemma 1 (see [2]). For ,？？ , one has Lemma 2. The operators , defined by (5) satisfy the following relations: Proof. By simple computation, we get Lemma 3. For , , and with , one has (i) ,(ii) ？ . Lemma 4. For , , one has Proof. Since , , and , we have which is required. 3. Some Local Approximation

Abstract:
A new estimate for the degree of approximation of a function class by means of its Fourier series has been determined. Here, we extend the results of Singh and Mahajan (2008) which in turn generalize the result of Lal and Yadav (2001). Some corollaries have also been deduced from our main theorem. 1. Introduction The degree of approximation of a function belonging to various classes using different summability method has been determined by several investigators like Khan [1, 2], V. N. Mishra and L. N. Mishra [3], Mishra et al. [4–6], and Mishra [7, 8]. Summability techniques were also applied on some engineering problems; for example, Chen and Jeng [9] implemented the Cesàro sum of order and , in order to accelerate the convergence rate to deal with the Gibbs phenomenon, for the dynamic response of a finite elastic body subjected to boundary traction. Chen and Hong [10] used Cesàro sum regularization technique for hyper singularity of dual integral equation. Summability of Fourier series is useful for engineering analysis, for example, [11]. Recently, Mursaleen and Mohiuddine [12] discussed convergence methods for double sequences and their applications in various fields. In sequel, Alexits [13] studied the degree of approximation of the functions in class by the Cesàro means of their Fourier series in the sup-norm. Chandra ([14, 15]), Mohapatra and Chandra ([16, 17]), and Szal [18] have studied the approximation of functions in H？lder metric. Mishra et al. [6] used the technique of approximation of functions in measuring the errors in the input signals and the processed output signals. In 2008, Singh and Mahajan [19] studied error bound of periodic signals in the H？lder metric and generalized the result of Lal and Yadav [20] under much more general assumptions. Analysis of signals or time functions is of great importance, because it conveys information or attributes of some phenomenon. The engineers and scientists use properties of Fourier approximation for designing digital filters. Especially, Psarakis and Moustakides [21] presented a new based method for designing the finite impulse response (FIR) digital filters and got corresponding optimum approximations having improved performance. We also discuss an example when the Fourier series of the signal has Gibbs phenomenon. For a -periodic signal , periodic integrable in the sense of Lebesgue. Then the Fourier series of is given by with th partial sum called trigonometric polynomial of degree (or order) and given by The conjugate series of Fourier series (1) is given by with th partial sum . Let and

Abstract:
We study a certain integral modification of well-known Baskakov operators with weight function of beta basis function. We establish rate of convergence for these operators for functions having derivative of bounded variation. Also, we discuss Stancu type generalization of these operators. 1. Introduction The integral modification of Baskakov operators having weight function of some beta basis function are defined as the following: for , , where being the Dirac delta function. The operators defined by (1) were introduced by Gupta [1]; these operators are different from the usual Baskakov-Durrmeyer operators. Actually these operators satisfy condition , where and are constants. In [1], the author estimated some direct results in simultaneous approximation for these operators (1). In particular case , the operators (1) reduce to the operators studied in [2, 3]. In recent years a lot of work has been done on such operators. We refer to some of the important papers on the recent development on similar type of operators [4–9]. The rate of convergence for certain Durrmeyer type operators and the generalizations is one of the important areas of research in recent years. In present article, we extend the studies and here we estimate the rate of convergence for functions having derivative of bounded variation. We denote ; then, in particular, we have By we denote the class of absolutely continuous functions defined on the interval such that,(i) , .(ii)having a derivative on the interval coinciding a.e. with a function which is of bounded variation on every finite subinterval of . It can be observed that all function possess for each a representation 2. Rate of Convergence for Lemma 1 (see [1]). Let the function , , be defined as Then it is easily verified that, for each , , and , and also the following recurrence relation holds: From the recurrence relation, it can be easily be verified that for all , we have . Remark 2. From Lemma 1, using Cauchy-Schwarz inequality, it follows that Lemma 3. Let and be the kernel defined in (1). Then for being sufficiently large, one has ？(a) . ？(b) . Proof. First we prove (a); by using Lemma 1, we have The proof of (b) is similar; we omit the details. Theorem 4. Let , , and . Then for being sufficiently large, we have where the auxiliary function is given by denotes the total variation of on . Proof. By the application of mean value theorem, we have Also, using the identity where we can see that Also, Substitute value of from (12) in (11) and using (14) and (15), we get Using Lemma 1 and Remark 2, we obtain On applying Lemma 3

Abstract:
In this paper, we determine the error bounds of conjugate signals between input periodic signals and processed output signals, whenever signals belong to $Lip\, (\alpha ,\, r)$ -class and as a processor we have taken almost generalized N\"orlund means using head bounded variation sequences and rest bounded variation sequences. The results obtained in this paper further extend several known results on linear operators.

Abstract:
We study the convergence of these operators in a weighted space of functions on a positive semi-axis and estimate the approximation by using a new type of weighted modulus of continuity and error estimation.