• Nonlinear Functional Analysis and Applications
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• 제29권3호
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• pp.867-883
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• 2024

The objective of this article is to study the general set-valued nonlinear variational-hemivariational inequalities and investigate the gap function, regularized gap function and Moreau-Yosida type regularized gap functions for the general set-valued nonlinear variational-hemivariational inequalities, and also discuss the error bounds for such inequalities using the characteristic of the Clarke generalized gradient, locally Lipschitz continuity, inverse strong monotonicity and Hausdorff Lipschitz continuous mappings.

• Honam Mathematical Journal
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• 제31권2호
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• pp.239-245
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• 2009

In this paper, we introduce the notions of m-semiopen sets and M-semicontinuous functions on spaces with minimal structures and study some properties of such notions. In particular, we investigate characterizations for the M-semicontinuous function and the relationship between M-continuity and M-semicontinuity.

• Kyungpook Mathematical Journal
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• 제62권3호
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• pp.467-484
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• 2022

In this work, we define bivariate Bernstein-Kantorovich type operators on a triangular domain and obtain some approximation results for these operators. We start off by computing some moment estimates and prove a Korovkin type convergence theorem. Then, we estimate the rate of convergence using the partial and complete modulus of continuity, and derive a Voronovskaya-type asymptotic theorem. Further, we calculate the order of approximation with regard to the Peetre's K-functional and a Lipschitz type class. In addition, we construct the associated GBS type operators and compute the rate of approximation using the mixed modulus of continuity and class of the Lipschitz of Bögel continuous functions for these operators. Finally, we use the two operators to approximate example functions in order to compare their convergence.

• Journal of the Chungcheong Mathematical Society
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• 제24권3호
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• pp.409-415
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• 2011

We introduce the notion of weakly quasi generalized continuous functions, and investigate properties for the continuity.

• East Asian mathematical journal
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• 제37권1호
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• pp.109-122
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• 2021

We establish existence and uniqueness of Green functions for flow velocity of stationary Stokes systems, under a continuity assumption of weak solutions to the system, in a bounded domain such that the divergence equation is solvable there. We also obtain pointwise bounds of the Green functions.

• The Pure and Applied Mathematics
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• 제19권4호
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• pp.423-435
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• 2012

We give some properties of weak Bloch functions and also give some properties of ${\phi}$-uniform domains and ${\phi}$-John domains in terms of moduli of continuity of Bloch functions and weak Bloch functions.

• Korean Journal of Mathematics
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• 제14권2호
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• pp.249-258
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• 2006

The weakened forms of the (${\theta},s$)-continuous function are introduced and their basic properties are investigated in concern with the other weakened continuous function. The open property of a function and the extremal disconnectedness of the spaces are crucial tools for the survey of these functions.

• International Journal of Fuzzy Logic and Intelligent Systems
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• 제9권2호
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• pp.83-93
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• 2009

Recently, El-Naschie has shown that the notion of fuzzy topology may be relevant to quantum paretical physics in connection with string theory and E-infinity space time theory. In this paper, we study the concepts of r-fuzzy semi-I-open, r-fuzzy pre-I-open, r-fuzzy $\alpha$-I-open and r-fuzzy $\beta$-I-open sets, which is properly placed between r-fuzzy openness and r-fuzzy $\alpha$-I-openness (r-fuzzy pre-I-openness) sets regardless the fuzzy ideal topological space in Sostak sense. Moreover, we give a decomposition of fuzzy continuity, fuzzy ideal continuity and fuzzy ideal $\alpha$-continuity, and obtain several characterization and some properties of these functions. Also, we investigate their relationship with other types of function.

• Journal of Electrical Engineering and Technology
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• 제10권2호
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• pp.676-687
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• 2015

Path planning algorithms are used to allow mobile robots to avoid obstacles and find ways from a start point to a target point. The general path planning algorithm focused on constructing of collision free path. However, a high continuous path can make smooth and efficiently movements. To improve the continuity of the path, the searched waypoints are connected by the proposed polynomial interpolation. The existing polynomial interpolation methods connect two points. In this paper, point groups are created with three points. The point groups have each polynomial. Polynomials are made by matching the differential values and simple matrix calculation. Membership functions are used to distribute the weight of each polynomial at overlapped sections. As a result, the path has $G^2$ continuity. In addition, the proposed method can analyze path numerically to obtain curvature and heading angle. Moreover, it does not require complex calculation and databases to save the created path.

• East Asian mathematical journal
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• 제23권1호
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• pp.103-110
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• 2007

The purpose of this paper is to introduce the concept of fuzzy set connected functions and investigate their properties.