• Journal of applied mathematics & informatics
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• v.19 no.1_2
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• pp.453-456
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• 2005

It is known that the classical Fatou's lemma and Lebesgue convergence theorem do not require the assumption that J1. is finite. In this note, we show that the assumption $\mu$(X) < $\infty$ cannot be replaced with a weaker assumption to prove Fatou's lemma and Lebesgue convergence theorem for a sequence of set-valued measurable function suggested by Zhang and Wang (Fuzzy Sets and Systems 56(1993) 237-241).

• Journal of applied mathematics & informatics
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• v.27 no.5_6
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• pp.1371-1379
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• 2009

In this paper, we introduce a relaxed hybrid-type$\eta$-f-${\alpha}$-pseudomo-notonicity. By using the KKM-technique, we establish some existence results for set-valued variational-like inequalities with $\eta-f-\alpha$-pseudomonotone, relaxed $\eta-f-\alpha$-pseudomonotone, Fan-KKM Theorem.

• Korean Journal of Mathematics
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• v.25 no.3
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• pp.389-403
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• 2017

The purpose of the present paper is to introduce and study new subclasses of analytic functions which generalize the classes of Janowski functions with respect to k-symmetric points. We also study certain interesting properties like covering theorem, convolution condition, neighborhood results and argument theorem.

• Journal of the Korean Mathematical Society
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• v.45 no.2
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• pp.313-329
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• 2008

In this paper, we study duality in the absolute Schur algebras that were first introduced in [1] and extended in [5]. This is done in a way analogous to the classical Schatten's Theorem on the Banach space $B(l_2)$ of bounded linear operators on $l_2$ involving the duality relation among the class of compact operators K, the trace class $C_1$ and $B(l_2)$. We also study the reflexivity in such the algebras.

• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.743-751
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• 2007

The aim of this article is to derive twenty five transformation formulas in the form of a single result for the triple hypergeometric series $X_8$ introduced earlier by Exton. The results are derived with the help of generalized Watson#s theorem obtained earlier by Lavoie et al. An interesting special cases are also pointed out.

• Journal of the Korean Mathematical Society
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• v.57 no.2
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• pp.359-381
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• 2020

In this paper we established new results of existence of conditional expectation for closed convex and unbounded Pettis integrable random sets without assuming the Radon Nikodym property of the Banach space. As application, new versions of multivalued Lévy's martingale convergence theorem are proved by using the Slice and the linear topologies.

• East Asian mathematical journal
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• v.32 no.5
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• pp.701-716
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• 2016

We establish a tripled coincidence and common tripled fixed point theorem for hybrid pair of mappings satisfying new contractive condition. To find tripled coincidence points, we do not use the continuity of any mapping involved therein. An example is also given to validate our result. We improve, extend and generalize several known results.

• Communications of the Korean Mathematical Society
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• v.14 no.4
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• pp.843-850
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• 1999

The object of this paper is to give certain classes of pre-sumably new product formulas involving the generalized hypergeo-metric series by modifying the elementary method suggested by Bai-ley.

• Journal of the Korean Mathematical Society
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• v.43 no.6
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• pp.1169-1181
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• 2006

We introduce a new biharmonic kernel for the upper half plane, and then study the properties of its relevant potentials, such as the convergence in the mean and the boundary behavior. Among other things, we shall see that Fatou's theorem is valid for these potentials, so that the biharmonic Poisson kernel resembles the usual Poisson kernel for the upper half plane.

• Korean Journal of Mathematics
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• v.26 no.2
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• pp.271-283
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• 2018

In this paper, we generelize the Olsen's density theorem to any measurable set, allowing us to extend the main results of H.K. Baek in (Proc. Indian Acad. Sci. (Math. Sci.) Vol. 118, (2008), pp. 273-279.). In particular, we tried through these results to improve the decomposition theorem of Besicovitch's type for the regularities of multifractal Hausdorff measure and packing measure.