• 대한수학회보
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• 제55권2호
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• pp.367-378
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• 2018

In this paper, we study m-isometric Toeplitz operators $T_{\varphi}$ with rational symbols. We characterize m-isometric Toeplitz operators $T_{\varphi}$ by properties of the rational symbols ${\varphi}$. In addition, we give a necessary and sufficient condition for Toeplitz operators $T_{\varphi}$ with analytic symbols ${\varphi}$ to be m-expansive or m-contractive. Finally, we give some results for m-expansive and m-contractive Toeplitz operators $T_{\varphi}$ with trigonometric polynomial symbols ${\varphi}$.

• Journal of applied mathematics & informatics
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• 제30권5_6호
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• pp.809-820
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• 2012

We establish a coincidence and a common fixed point result for four mappings involving a (${\psi}$, ${\varphi}$)-weak contractive condition type on a complete metric space. We take on ${\psi}$ and ${\varphi}$ the same conditions given by Popescu [Fixed points for (${\psi}$, ${\varphi}$)-weak contractions, Appl. Math. Lett. 24 (2011), 1-4].

• 충청수학회지
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• 제29권3호
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• pp.417-428
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• 2016

We discuss and obtain some existence theorems of unique point of coincidence for two mappings satisfying ${\varphi}$-contractive conditions or ${\psi}$-${\phi}$-contractive conditions determined by semi-continuous functions on non-complete 2-metric spaces, in which the mappings do not satisfy commutativity and uniform boundedness. The obtained results generalize and improve many well-known and corresponding conclusions.

• Nonlinear Functional Analysis and Applications
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• 제26권3호
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• pp.601-610
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• 2021

A convergence theorem for a generalized 𝜑-weakly contractive mapping is proved which satisfy a generalized contraction condition on a complete metrically convex metric space. The result in this paper generalizes the relevant results due to Rhoades [18], Alber and Guerre-Delabriere [1], Khan and Imdad [14], Xue [20] and others. An illustrative example is also furnished in support of our main result.