• Title/Summary/Keyword: functional inequality

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STABILITY OF PARTIALLY PEXIDERIZED EXPONENTIAL-RADICAL FUNCTIONAL EQUATION

  • Choi, Chang-Kwon
    • Bulletin of the Korean Mathematical Society
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    • v.58 no.2
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    • pp.269-275
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    • 2021
  • Let ℝ be the set of real numbers, f, g : ℝ → ℝ and �� ≥ 0. In this paper, we consider the stability of partially pexiderized exponential-radical functional equation $$f({\sqrt[n]{x^N+y^N}})=f(x)g(y)$$ for all x, y ∈ ℝ, i.e., we investigate the functional inequality $$\|f({\sqrt[n]{x^N+y^N}})-f(x)g(y)\|{\leq}{\epsilon}$$ for all x, y ∈ ℝ.

MULTIPLICITY RESULTS AND THE M-PAIRS OF TORUS-SPHERE VARIATIONAL LINKS OF THE STRONGLY INDEFINITE FUNCTIONAL

  • Jung, Tack-Sun;Choi, Q-Heung
    • Journal of the Korean Society for Industrial and Applied Mathematics
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    • v.12 no.4
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    • pp.239-247
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    • 2008
  • Let $I{\in}C^{1,1}$ be a strongly indefinite functional defined on a Hilbert space H. We investigate the number of the critical points of I when I satisfies two pairs of Torus-Sphere variational linking inequalities and when I satisfies m ($m{\geq}2$) pairs of Torus-Sphere variational linking inequalities. We show that I has at least four critical points when I satisfies two pairs of Torus-Sphere variational linking inequality with $(P.S.)^*_c$ condition. Moreover we show that I has at least 2m critical points when I satisfies m ($m{\geq}2$) pairs of Torus-Sphere variational linking inequalities with $(P.S.)^*_c$ condition. We prove these results by Theorem 2.2 (Theorem 1.1 in [1]) and the critical point theory on the manifold with boundary.

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A Line-integral Fuzzy Lyapunov Functional Approach to Sampled-data Tracking Control of Takagi-Sugeno Fuzzy Systems

  • Kim, Han Sol;Joo, Young Hoon
    • Journal of Electrical Engineering and Technology
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    • v.13 no.6
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    • pp.2521-2529
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    • 2018
  • This paper deals with a sampled-data tracking control problem for the Takagi-Sugeno fuzzy system with external disturbances. We derive a stability condition guaranteeing both asymptotic stability and H-infinity tracking performance by employing a newly proposed time-dependent line-integral fuzzy Lyapunov-Krasovskii functional. A new integral inequality is also introduced, by which the proposed stability condition is formulated in terms of linear matrix inequalities. Finally, the effectiveness of the proposed method is demonstrated through a simulation example.

JORDAN *-HOMOMORPHISMS BETWEEN UNITAL C*-ALGEBRAS

  • Gordji, Madjid Eshaghi;Ghobadipour, Norooz;Park, Choon-Kil
    • Communications of the Korean Mathematical Society
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    • v.27 no.1
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    • pp.149-158
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    • 2012
  • In this paper, we prove the superstability and the generalized Hyers-Ulam stability of Jordan *-homomorphisms between unital $C^*$-algebras associated with the following functional equation$$f(\frac{-x+y}{3})+f(\frac{x-3z}{c})+f(\frac{3x-y+3z}{3})=f(x)$$. Morever, we investigate Jordan *-homomorphisms between unital $C^*$-algebras associated with the following functional inequality $${\parallel}f(\frac{-x+y}{3})+f(\frac{x-3z}{3})+f(\frac{3x-y+3z}{3}){\parallel}\leq{\parallel}f(x)\parallel$$.

HYBRID INERTIAL CONTRACTION PROJECTION METHODS EXTENDED TO VARIATIONAL INEQUALITY PROBLEMS

  • Truong, N.D.;Kim, J.K.;Anh, T.H.H.
    • Nonlinear Functional Analysis and Applications
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    • v.27 no.1
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    • pp.203-221
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    • 2022
  • In this paper, we introduce new hybrid inertial contraction projection algorithms for solving variational inequality problems over the intersection of the fixed point sets of demicontractive mappings in a real Hilbert space. The proposed algorithms are based on the hybrid steepest-descent method for variational inequality problems and the inertial techniques for finding fixed points of nonexpansive mappings. Strong convergence of the iterative algorithms is proved. Several fundamental experiments are provided to illustrate computational efficiency of the given algorithm and comparison with other known algorithms

STUDY OF SOME GENERALIZED h-VARIATIONAL INEQUALITY PROBLEMS IN H-PSEUDOSPACE

  • Das, Prasanta K.;Mishra, Satya N.;Samal, Sapan K.
    • Nonlinear Functional Analysis and Applications
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    • v.26 no.3
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    • pp.475-496
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    • 2021
  • The main aim is to define a new class of generalized h-variational inequality problems and its generalized h-variational inequality problems. We define the class of h-𝜂-invex set, h-𝜂-invex function and H-pseudospace. Existence of the solution of the problems are established in H-pseudospace with the help of H-KKM mapping theorem and HC*-condition of 𝜂 associated with the function h.

APPROXIMATION METHODS FOR SOLVING SPLIT EQUALITY OF VARIATIONAL INEQUALITY AND f, g-FIXED POINT PROBLEMS IN REFLEXIVE BANACH SPACES

  • Yirga Abebe Belay;Habtu Zegeye;Oganeditse A. Boikanyo
    • Nonlinear Functional Analysis and Applications
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    • v.28 no.1
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    • pp.135-173
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    • 2023
  • The purpose of this paper is to introduce and study a method for solving the split equality of variational inequality and f, g-fixed point problems in reflexive real Banach spaces, where the variational inequality problems are for uniformly continuous pseudomonotone mappings and the fixed point problems are for Bregman relatively f, g-nonexpansive mappings. A strong convergence theorem is proved under some mild conditions. Finally, a numerical example is provided to demonstrate the effectiveness of the algorithm.