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Vol.15 No.2
Abstract
In this paper, we obtain the general solution and the stability of the cubic functional equation f(2x + y, 2z + w) + f(2x - y, 2z - w) = 2f(x + y, z + w) + 2f(x - y, z - w) + 12f(x, z). The cubic form <TEX>$f(x,\;y)\;=\;ax^3\;+\;bx^2y\;+\;cxy^2\;+\;dy^3$</TEX> is a solution of the above functional equation.
Abstract
A semi local convergence analysis is provided for Newton's method in a Banach space setting. The operators involved are only locally Holderian. We make use of a point-based approximation and center-Holderian hypotheses. This approach can be used to approximate solutions of equations involving nonsmooth operators.
Abstract
A pebbling step on a graph consists of removing two pebbles from one vertex and placing one pebble on an adjacent vertex. The covering cover pebbling number of a graph is the smallest number of pebbles, such that, however the pebbles are initially placed on the vertices of the graph, after a sequence of pebbling moves, the set of vertices with pebbles forms a covering of G. In this paper we find the covering cover pebbling number of n-cube and diameter two graphs. Finally we give an upperbound for the covering cover pebbling number of graphs of diameter d.
Abstract
The purpose of this paper is to prove some common fixed point theorems for finite number of discontinuous, noncompatible mappings on non complete Menger spaces. Our results extend, improve and generalize several known results in Menger spaces. We give formulas for total number of commutativity conditions for finite number of mappings.
Abstract
In the present paper we introduce a Jensen type quartic functional equation and then investigate the generalized Hyers-Ulam stability problem for the equation.
Abstract
This paper presents characterizations of the Weibull distribution by the independence of record values. We prove that <TEX>$X\;{\in}\;W\;EI ({\alpha})$</TEX>, if and only if <TEX>$\frac {X_{U(n+l)}} {X_{U(n+1)}\;+\;X_{U(n)}}$</TEX> and <TEX>$X_{U(n+1)}$</TEX> for <TEX>$n{\geq}1$</TEX> are independent or <TEX>$\frac {X_{U(n)}} {X_{U(n+1)}\;+\;X_{U(n)}}$</TEX> and <TEX>$X_{U(n+1)}$</TEX> for <TEX>$n{\geq}1$</TEX> are independent. And also we establish that <TEX>$X\;{\in}\;W\;EI({\alpha})$</TEX>, if and only if <TEX>$\frac {X_{U(n+1)}\;-\;X_{U(n)}} {X_{U(n+1)}\;+\;X_{U(n)}}$</TEX> and <TEX>$X_{U(n+1)}$</TEX> for <TEX>$n{\geq}1$</TEX> are independent.
Abstract
In this paper we generalize the superstability of the exponential functional equation proved by J. Baker et al. [2], that is, we solve an exponential type functional equation <TEX>$$f(x+y)\;=\;a^{xy}f(x)f(y)$$</TEX> and obtain the superstability of this equation. Also we generalize the stability of the exponential type equation in the spirt of R. Ger[4] of the following setting <TEX>$$|{\frac{f(x\;+\;y)}{{a^{xy}f(x)f(y)}}}\;-\;1|\;{\leq}\;{\delta}.$$</TEX>
Abstract
Let A be a noncommutative Banach algebra. Suppose there exists a continuous linear Jordan derivation <TEX>$D\;:\;A{\rightarrow}A$</TEX> such that <TEX>$D(x)[D(x),x]^2\;{\in}\;rad(A)$</TEX> or <TEX>$[D(x), x]^2 D(x)\;{\in}\;rad(A)$</TEX> for all <TEX>$x\;{\in}\ A$</TEX>. In this case, we have <TEX>$D(A)\;{\subseteq}\;rad(A)$</TEX>.
Abstract
In [1], Mishra and Wang established relationships between vector variational-like inequality problems and non-smooth vector optimization problems under non-smooth invexity in finite-dimensional spaces. In this paper, we generalize recent results of Mishra and Wang to infinite-dimensional case.