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ISSN : 1226-0657
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Vol.26 No.2
Abstract
In this paper, a version of the boundary Schwarz Lemma for the holomorphic function belonging to <TEX>$\mathcal{N}$</TEX>(<TEX>${\alpha}$</TEX>) is investigated. For the function <TEX>$f(z)=z+c_2z^2+C_3z^3+{\cdots}$</TEX> which is defined in the unit disc where <TEX>$f(z){\in}\mathcal{N}({\alpha})$</TEX>, we estimate the modulus of the angular derivative of the function f(z) at the boundary point b with <TEX>$f(b)={\frac{1}{b}}\int\limits_0^b$</TEX> f(t)dt. The sharpness of these inequalities is also proved.
Abstract
In this paper, we introduce quasiuniform convergence structure induced by operators on ecl-premonoid (L, <TEX>${\ast}$</TEX>, <TEX>${\odot}$</TEX>). Moreover, we obtain <TEX>$(L,\;{\ast},\;{\odot})-quasiuniform$</TEX> convergence structure induced by two <TEX>$(L,\;{\ast},\;{\odot})-quasiuniform$</TEX> convergence structures and gives their examples.
Abstract
In this paper we introduce the reciprocal-negative Fermat's equation induced by the famous equation in the Fermat's Last Theorem, establish the general solution in the simplest cases and the differential solution to the equation, and investigate, then, the generalized Hyers-Ulam stability in a <TEX>$quasi-{\beta}-normed$</TEX> space with both the direct estimation method and the fixed point approach.
Abstract
In this paper, we prove some common fixed point theorems for pairs of weakened compatible mappings (subcompatible and occasionally weakly compatible mappings) satisfying a generalized <TEX>${\phi}-weak$</TEX> contraction condition involving various combinations of the metric functions. In fact, our results improve the results of Jain et al.. Also we provide an example for validity of our results.