• The Pure and Applied Mathematics
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• v.29 no.4
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• pp.335-352
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• 2022

In this paper, we give an extended version of fixed point results for 𝜃-contraction and 𝜃-𝜙-contraction and define a new type of contraction, namely, cyclic 𝜃-contraction and cyclic 𝜃-𝜙-contraction in a complete metric space. Moreover, we prove the existence of best proximity point for cyclic 𝜃-contraction and cyclic 𝜃-𝜙-contraction. Also, we establish best proximity result in the setting of uniformly convex Banach space.

• Nonlinear Functional Analysis and Applications
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• v.27 no.4
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• pp.709-730
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• 2022

We consider the nonlinear matrix equation (NMEs) of the form 𝓤 = 𝓠 + Σ^k_i=1 𝓐^*_iℏ(𝓤)𝓐_i, where 𝓠 is n × n Hermitian positive definite matrices (HPDS), 𝓐₁, 𝓐₂, . . . , 𝓐_m are n × n matrices, and ~ is a nonlinear self-mappings of the set of all Hermitian matrices which are continuous in the trace norm. We discuss a sufficient condition ensuring the existence of a unique positive definite solution of a given NME and demonstrate this sufficient condition for a NME 𝓤 = 𝓠 + 𝓐^*₁(𝓤²/900)𝓐₁ + 𝓐^*₂(𝓤²/900)𝓐₂ + 𝓐^*₃(𝓤²/900)𝓐₃. In order to do this, we define 𝓕𝓖_w-contractive conditions and derive fixed points results based on aforesaid contractive condition for a mapping in extended Branciari b-metric distance followed by two suitable examples. In addition, we introduce weak well-posed property, weak limit shadowing property and generalized Ulam-Hyers stability in the underlying space and related results.

• Journal of Korean Society for Geospatial Information Science
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• v.6 no.1 s.11
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• pp.11-17
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• 1998

Recently, 3D GIS based on 3D geo-processing methodology and Internet environment are emerging issues in GIS fields. To design and implement 3D GIS, the strategic linkage of Java and VRML is first regarded: 3D feature format definition in the passion of conventional GIS including aspatial attributes, 3B feature indexing, 3D analytical operators such as selection, buffering, and Near, Metric operation such as distance measurement and statistical description, and 3D visualization. In 3D feature format definition, the following aspects are implemented: spatial information for 3D primitives extended from 2D primitives, multimedia data, object texture or color of VRML specification. DXF-format GIS layers with additional attributes are converted to 3D feature format and imported into this system. While, 3D analytical operators are realized in the form of 3D buffering with respect to user-defined point, line, polygon, and 3D objects, and 3D Near functions; furthermore, 'Lantern operator' is newly introduced in this 3D GIS. Because this system is implemented by Java applet, any client with Java-enable browser including VRML browser plug-in can utilize the new style of 3D GIS function in the virtual space. Conclusively, we present prototype of WWW-based 3D GIS, and this approach will be contribute to development of core modules on the stage of concept establishment and of real application model in future.