On the contraction operator

Bu çalışmanın amacı, X bir tam metrik uzay, T işlemi X metrik uzayından kendi içine bir dönüşüm (T:X->X) olmak üzere, Banach daralma operatörünü kapsayan ve her $x,yin X$ için geçerli, $rho[Tx,Ty] leq alpha {rho(x,Tx)+rho(y,Ty)}$, $alpha in [0,frac{1}{2}]$dönüşümünü sağlayan genelleştirilmiş $f_{lambda}$ daralma operatör sınıfını tanımlamak incelemektedir. T işleminin [3] deki genelleştirilmiş daralma işlemini sağladığı X'in bir noktasını sabit bıraktığı gösterilmiştir.

Daralma operatörü üzerine

The purpose of this study is to define and investigate a class of generalized $f_{lambda}$ contraction operators, which includes the Banach contraction operator and the mapping, $rho[Tx,Ty] leq alpha {rho(x,Tx)+rho(y,Ty)}$,$alpha in [0,frac{1}{2}]$which holds for all $x,yin X$. Here, X is a complete metric space and T is a mapping of X into itself. It is proved that the operator T leaves exactly one point of X fixed and satisfies the generalized contractions in [3].

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