New Type of Generalised B-difference Sequence Space
Rayees Ahmad and Syed Najam u Hasan |
ABSTRACT: The sequence space rq ∆up have been defined and introduced by Ganie et al (see, new paranormed sequence space and some matrix transformations, Int. J. Mod. Math. Sci., 8(2)(2013), 185-194 [17]) and have studied its various properties. The aim of the present paper is to introduce the new generalized difference sequence space rBq (u,p) . We have shown rBq (u,p) to be complete and also have shown that it to be linearly isomorphic to the space l(p). Also, investigations have been made for computing its α-, β- and γ-duals and constructed its basis..
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A Study of Generalized Fractional Derivative Operator Involving Aleph(ℵ) -function, General Class of Multivariable Polynomials and Certain Multiplication Formulae for Aleph(ℵ) -Function of Multivariable Functions
Sanjay Bhatter and Rakesh Kumar Bohra |
ABSTRACT: The aim of the present paper is to create two new and useful theorems by using the generalized differential operator Dmk,α,x involving a general multivariable polynomial and Aleph(ℵ) -function. Two multivariable formulae for Aleph(ℵ) function of multivariable functions have been obtained as special cases of our main result.
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An Iterative Algorithm for a System of Generalized Mixed Variational Inclusion Problems
Mohd Iqbal Bhat and Sumeera Shafi |
ABSTRACT: We introduce and study a system of generalized mixed variational inclusion problems in Banach space. We define a class of (H(..,.),η) -monotone operators and its associated class of resolvent operators. Further, we prove that the associated resolvent operator is single-valued and Lipschitz continuous. Using resolvent operator technique, we propose an iterative algorithm for solving the system. Furthermore, we prove that the sequences generated by the algorithm converge strongly to a solution of the system. The results presented in this paper extend and unify the related known results in the literature.
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Fractional Derivative Associated with the Multivariable A-Function, the Extension of Zeta-function and Multivariable Polynomials
Ayant Frederic
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ABSTRACT: The aim of present paper is to derive a fractional derivative of the multivariable A-function defined by Gautam et al [2], associated with a general class of multivariable polynomials of Srivastava et al [8], the A-function of one variable defined by Gautam et al [1], the generalized incomplete hypergeometric function and the generalized Lauricella functions of Srivastava and Daoust [9]. Several particular cases will be given. The results derived here are of a very general nature and hence encompass several cases of interest hittherto scattered in the literature.
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Generating Ordered Maps via Supra Topological Ordered Spaces
M. E. El-Shafei, M. Abo-Elhamayel and T. M. Al-shami |
ABSTRACT: We employ the notions of supra α-open sets and increasing (decreasing, balancing) sets in introducing various forms of supra continuous (supra open, supra closed, supra homeomorphism) maps in supra topological ordered spaces. We illustrate relationships among these concepts separately and give equivalent conditions for each one of them. Moreover, we investigate under what conditions these maps preserve some separation axioms between supra topological ordered spaces.
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Modified Ratio Estimator for Estimating Population Mean Using Auxiliary Information in Survey Sampling
Mir Subzar, S. Maqbool, N A Sofi, T A Raja and Zaffar Bashir |
ABSTRACT: In this paper we propose a family of modified ratio type estimator for estimating the population mean of the study variable using the auxiliary information of population standard deviation, coefficient of skewness, correlation coefficient, coefficient of kurtosis and coefficient of variation. The properties associated with the proposed estimator is evaluated through MSE and bias. We also provide an empirical study for illustration and verification.
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