• Journal of the Korean Mathematical Society
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• v.45 no.3
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• pp.841-858
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• 2008

In this paper, we introduce two classes of generalized variational-like inequalities with compositely monotone multifunctions in Banach spaces. Using the KKM-Fan lemma and the Nadler's result, we prove the existence of solutions for generalized variational-like inequalities with compositely relaxed ${\eta}-{\alpha}$ monotone multifunctions in reflexive Banach spaces. On the other hand we also derive the solvability of generalized variational-like inequalities with compositely relaxed ${\eta}-{\alpha}$ semimonotone multi functions in arbitrary Banach spaces by virtue of the Kakutani-Fan-Glicksberg fixed-point theorem. The results presented in this paper extend and improve some earlier and recent results in the literature.

• Communications of the Korean Mathematical Society
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• v.28 no.4
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• pp.819-825
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• 2013

Similarly to Tychonoff product, we introduce the concept of generalized product topology which is different from the notion of product of generalized topologies in [$\acute{A}$. $Cs\acute{a}sz\acute{a}r$, Acta Math. Hungar. 123 (2009), 127-132] for generalized topology and obtain some properties about it. Besides, we prove that connectedness, ${\sigma}$-connectedness and ${\alpha}$-connectedness are all preserved under this product.

• Journal of applied mathematics & informatics
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• v.32 no.3_4
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• pp.405-426
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• 2014

The concept of interval-valued (${\alpha},{\beta}$)-fuzzy ideals, interval-valued (${\alpha},{\beta}$)-fuzzy generalized bi-ideals are introduced in LA-semigroups, using the ideas of belonging and quasi-coincidence of an interval-valued fuzzy point with an interval-valued fuzzy set and some related properties are investigated. We define the lower and upper parts of interval-valued fuzzy subsets of an LA-semigroup. Regular LA-semigroups are characterized by the properties of the lower part of interval-valued (${\in},{\in}{\vee}q$)-fuzzy left ideals, interval-valued (${\in},{\in}{\vee}q$)-fuzzy quasi-ideals and interval-valued (${\in},{\in}{\vee}q$)-fuzzy generalized bi-ideals. Main Facts.

• Journal of applied mathematics & informatics
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• v.31 no.5_6
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• pp.835-852
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• 2013

In this paper, we have considered a class of constrained non-smooth multiobjective fractional programming problem involving support functions under generalized convexity. Also, second order Mond Weir type dual and Schaible type dual are discussed and various weak, strong and strict converse duality results are derived under generalized class of second order (F, ${\alpha}$, ${\rho}$, $d$)-V-type I functions. Also, we have illustrated through non-trivial examples that class of second order (F, ${\alpha}$, ${\rho}$, $d$)-V-type I functions extends the definitions of generalized convexity appeared in the literature.

• Communications of the Korean Mathematical Society
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• v.14 no.1
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• pp.121-134
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• 1999

Generalized nonnegative polynomials are defined as the products of nonnegative polynomials raised to positive real powers. The generalized degree can be defined in a natural way. We extend some results on Infinite-Finite range inequalities, Christoffel functions, and Nikolski type inequalities corresponding to weights W\ulcorner(x)=exp(-｜x｜\ulcorner), $\alpha$>0, to those for generalized nonnegative polynomials.

• Kyungpook Mathematical Journal
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• v.54 no.3
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• pp.387-399
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• 2014

We show that in quasi-topological spaces, separation axiom $T_2$ is equivalent to ${\alpha}-T_2$, $T_0$ is equivalent to semi - $T_0$, and semi - $T_{\frac{1}{2}}$ is equivalent to semi - $T_D$. Also, we give characterizations for ${\alpha}-T_1$, semi - $T_1$ and semi - $T_{\frac{1}{2}}$ generalized topological spaces.

• Journal of Applied and Pure Mathematics
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• v.4 no.1_2
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• pp.1-7
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• 2022

A mapping T : R → R (not necessarily additive) is called multiplicative left 𝛼-centralizer if T(xy) = T(x)𝛼(y) for all x, y ∈ R. A mapping F : R → R (not necessarily additive) is called multiplicative (generalized)(𝛼, 𝛽)-derivation if there exists a map (neither necessarily additive nor derivation) f : R → R such that F(xy) = F(x)𝛼(y) + 𝛽(x)f(y) for all x, y ∈ R, where 𝛼 and 𝛽 are automorphisms on R. The main purpose of this paper is to study some algebraic identities with multiplicative (generalized) (𝛼, 𝛽)-derivations and multiplicative left 𝛼-centralizer on the left ideal of a prime ring R.

• Journal of applied mathematics & informatics
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• v.42 no.4
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• pp.879-897
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• 2024

The emergence of generalized square metrics in Finsler geometry can be attributed to various classification concerning (𝛼, 𝛽)-metrics. They have excellent geometric properties in Finsler geometry. Within the scope of this research paper, we have conducted an investigation into the generalized square metric denoted as $F(x,y)=\frac{[{\alpha}(x,y)+{\beta}(x,y)]^{n+1}}{[{\alpha}(x,y)]^n}$, focusing specifically on its application to the Finslerian hypersurface. Furthermore, the classification and existence of first, second, and third kind of hyperplanes of the Finsler manifold has been established.

• The Pure and Applied Mathematics
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• v.20 no.2
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• pp.117-127
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• 2013

As a generalization of fuzzy subsemigroups, the notion of ${\varepsilon}$-generalized fuzzy subsemigroups is introduced, and several properties are investigated. A condition for an ${\varepsilon}$-generalized fuzzy subsemigroup to be a fuzzy subsemigroup is considered. Characterizations of ${\varepsilon}$-generalized fuzzy subsemigroups are established, and we show that the intersection of two ${\varepsilon}$-generalized fuzzy subsemigroups is also an ${\varepsilon}$-generalized fuzzy subsemigroup. A condition for an ${\varepsilon}$-generalized fuzzy subsemigroup to be ${\varepsilon}$-fuzzy idempotent is discussed. Using a given ${\varepsilon}$-generalized fuzzy subsemigroup, a new ${\varepsilon}$-generalized fuzzy subsemigroup is constructed. Finally, the fuzzy extension of an ${\varepsilon}$-generalized fuzzy subsemigroup is considered.

• East Asian mathematical journal
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• v.32 no.3
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• pp.319-332
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• 2016

In this paper, we introduce the notion of generalized ${\alpha}-{\psi}$-Geraghty multivalued mappings and investigate the existence of a xed point of such multivalued mappings. We present a concrete example and an application on integral equations illustrating the obtained results.