• East Asian mathematical journal
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• 제28권5호
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• pp.533-541
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• 2012

A common fixed point result of Gregus type for subcompatible mappings defined on a complete linear metric space is obtained. The considered underlying space is generalized from Banach space to complete linear metric spaces, which include Banach space and complete metrizable locally convex spaces. Invariant approximation results have also been determined as its application.

• 대한수학회보
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• 제36권2호
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• pp.379-388
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• 1999

In this paper, we introduce a semi-metric on a normed almost linear space X via functional. And we prove that a normed almost linear space X is complete if and only if $V_X$ and $W_X$ are complete when X splits as X=$W_X$ + $V_X$. Also, we prove that the dual space $X^\ast$ of a normed almost linear space X is complete.

• Korean Journal of Mathematics
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• 제4권1호
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• pp.1-5
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• 1996

A strong Banach-Mackey property is established for ${\kappa}$-spaces including all complete and some non-complete metric linear spaces and some non-metrizable locally convex spaces. As applications of this result, a strong uniform boundedness result and a new Banach-Steinhaus type theorem are obtained.

• Journal of applied mathematics & informatics
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• 제19권1_2호
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• pp.485-492
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• 2005

In this paper, we obtain some common fixed point theorems for fuzzy mappings in complete metric linear spaces.

• Kyungpook Mathematical Journal
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• 제28권1호
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• pp.97-106
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• 1988

In the first section of this paper two common fixed point results for four nonlinear mappings which are pairwise commuting and only two of them being continuous have been given on a complete metric space and on a compact metric space respectively which generalize the results of Mukherjee [2] and Yeh [4]. Further two common fixed point theorems have been established for two finite families of non linear mappings, with only one family being continuous. In another section we extend Theorem 3 and Theorem 4 of Mukherjee [2] for common fixed point of four continuous mappings on a Hausdorff space and on a compact metric space respectively. In the same spaces, these two results have been further generalized for two finite families of continuous mappings.

• Kyungpook Mathematical Journal
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• 제55권4호
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• pp.909-931
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• 2015

This paper presents some new paranormed sequence spaces $X(r,s,t,p;{\Delta})$ where $X{\in}\{l_{\infty}(p),c(p),c_0(p),l(p)\}$ defined by using generalized means and difference operator. It is shown that these are complete linear metric spaces under suitable paranorms. Furthermore, the ${\alpha}$-, ${\beta}$-, ${\gamma}$-duals of these sequence spaces are computed and also obtained necessary and sufficient conditions for some matrix transformations from $X(r,s,t,p;{\Delta})$ to X. Finally, it is proved that the sequence space $l(r,s,t,p;{\Delta})$ is rotund when $p_n$ > 1 for all n and has the Kadec-Klee property.