• Korean Journal of Mathematics
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• v.27 no.4
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• pp.843-860
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• 2019

In the article, we present several new Hermite-Hadamard and Hermite-Hadamard-Fejér type inequalities for the exponentially (ħ, m)-convex functions via an extended generalized Mittag-Leffler function. As applications, some variants for certain typ e of fractional integral operators are established and some remarkable special cases of our results are also have been obtained.

• Honam Mathematical Journal
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• v.42 no.4
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• pp.653-665
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• 2020

In this paper, we establish new integral inequalities via Riemann-Liouville fractional integrals and Katugampola fractional integrals for the class of functions whose derivatives in absolute value are exponentially convex functions and exponentially s-convex functions in the second sense.

• Kyungpook Mathematical Journal
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• v.45 no.4
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• pp.491-502
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• 2005

The main purpose of this paper is to extend the exponentially convex functions which are defined and exponentially convex on a cylinderical neighborhood in the Heisenberg group. They are expanded in terms of an integral transform associated to the sub-Laplacian operator. Extension of such functions on abelian Lie group are studied in [15].

• Kyungpook Mathematical Journal
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• v.46 no.3
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• pp.337-343
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• 2006

In the present paper we shall prove that on a foundation *-semigroup S with an identity and with a locally bounded Borel measurable weight function ${\omega}$, the pointwise convergence and the uniform convergence of a sequence of ${\omega}$-bounded exponentially convex functions on S which are also continuous at the identity are equivalent.

• Journal of the Korean Mathematical Society
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• v.48 no.4
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• pp.775-795
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• 2011

The disturbance attenuation problem for a class of discretetime switched linear systems with exponential uncertainties via switched state feedback and switched dynamic output feedback is investigated, respectively. By using Taylor series approximation and convex polytope technique, exponentially uncertain discrete-time switched linear system is transformed into an equivalent switched polytopic model with additive norm bounded uncertainty. For such equivalent switched model, one designs its switching strategy and associated state feedback controllers and dynamic output feedback controllers so that whole switched model is asymptotical stabilization with H-in nity disturbance attenuation base on switched Lyapunov function and LMI approach. Finally, two numerical examples are presented to illustrate our results.