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ISSN : 1226-0657
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Vol.24 No.2
Abstract
The object of the present paper is to study generalized Z-recurrent manifolds. Some geometric properties of generalized Z-recurrent manifolds have been studied under certain curvature conditions. Finally, we give an example of a generalized Z-recurrent manifold.
Abstract
If q(z) is a polynomial of degree n with all zeros in the unit circle, then the self-reciprocal polynomial <TEX>$q(z)+x^nq(1/z)$</TEX> has all its zeros on the unit circle. One might naturally ask: where are the zeros of <TEX>$q(z)+x^nq(1/z)$</TEX> located if q(z) has different zero distribution from the unit circle? In this paper, we study this question when <TEX>$q(z)=(z-1)^{n-k}(z-1-c_1){\cdots}(z-1-c_k)+(z+1)^{n-k}(z+1+c_1){\cdots}(z+1+c_k)$</TEX>, where <TEX>$c_j$</TEX> > 0 for each j, and q(z) is a 'zeros dragged' polynomial from <TEX>$(z-1)^n+(z+1)^n$</TEX> whose all zeros lie on the imaginary axis.
Abstract
We establish a coupled coincidence point theorem for generalized compatible pair of mappings <TEX>$F,G:X{\times}X{\rightarrow}X$</TEX> under generalized symmetric Meir-Keeler contraction on a partially ordered metric space. We also deduce certain coupled fixed point results without mixed monotone property of <TEX>$F:X{\times}X{\rightarrow}X$</TEX>. An example supporting to our result has also been cited. As an application the solution of integral equations are obtain here to illustrate the usability of the obtained results. We improve, extend and generalize several known results.
Abstract
Shokri et al. [14] proved the Hyers-Ulam stability of bihomomorphisms and biderivations by using the direct method. It is easy to show that the definition of biderivations on normed 3-Lie algebras is meaningless and so the results of [14] are meaningless. In this paper, we correct the definition of biderivations and the statements of the results in [14], and prove the corrected theorems.
Abstract
In this paper, we solve the following quadratic <TEX>${\rho}-functional$</TEX> inequalities <TEX>${\parallel}f({\frac{x+y+z}{2}})+f({\frac{x-y-z}{2}})+f({\frac{y-x-z}{2}})+f({\frac{z-x-y}{2}})-f(x)-f(y)f(z){\parallel}$</TEX> (0.1) <TEX>${\leq}{\parallel}{\rho}(f(x+y+z)+f(x-y-z)+f(y-x-z)+f(z-x-y)-4f(x)-4f(y)-4f(z)){\parallel}$</TEX>, where <TEX>${\rho}$</TEX> is a fixed non-Archimedean number with <TEX>${\mid}{\rho}{\mid}$</TEX> < <TEX>${\frac{1}{{\mid}4{\mid}}}$</TEX>, and <TEX>${\parallel}f(x+y+z)+f(x-y-z)+f(y-x-z)+f(z-x-y)-4f(x)-4f(y)-4f(z){\parallel}$</TEX> (0.2) <TEX>${\leq}{\parallel}{\rho}(f({\frac{x+y+z}{2}})+f({\frac{x-y-z}{2}})+f({\frac{y-x-z}{2}})+f({\frac{z-x-y}{2}})-f(x)-f(y)f(z)){\parallel}$</TEX>, where <TEX>${\rho}$</TEX> is a fixed non-Archimedean number with <TEX>${\mid}{\rho}{\mid}$</TEX> < <TEX>${\mid}8{\mid}$</TEX>. Using the direct method, we prove the Hyers-Ulam stability of the quadratic <TEX>${\rho}-functional$</TEX> inequalities (0.1) and (0.2) in non-Archimedean Banach spaces and prove the Hyers-Ulam stability of quadratic <TEX>${\rho}-functional$</TEX> equations associated with the quadratic <TEX>${\rho}-functional$</TEX> inequalities (0.1) and (0.2) in non-Archimedean Banach spaces.