• 충청수학회지
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• 제32권2호
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• pp.195-205
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• 2019

We consider additive mappings similar to derivations on Banach ${\ast}$-algebras and we will first study the conditions for such additive mappings on Banach ${\ast}$-algebras. Then we prove some theorems concerning approximate linear mappings of derivation-type on Banach ${\ast}$-algebras. As an application, approximate linear mappings of derivation-type on $C^{\ast}$-algebra are characterized.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제28권2호
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• pp.91-102
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• 2021

In this paper, we introduce Lie bracket Jordan derivations in Banach Jordan algebras. Using the direct method and the fixed point method, we prove the Hyers-Ulam stability of Lie bracket Jordan derivations in complex Banach Jordan algebras.

• Nonlinear Functional Analysis and Applications
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• 제27권1호
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• pp.83-97
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• 2022

In this paper, we introduce and study generalized mixed operator quasi-equilibrium problems(GMQOEP) in Hausdorff topological vector spaces and prove the existence results for the solution of (GMQOEP) in compact and noncompact settings by employing 1-person game theorems. Moreover, using coercive condition, hemicontinuity of the functions and KKM theorem, we prove new results on the existence of solution for the particular case of (GMQOEP), that is, generalized mixed operator equilibrium problem (GMOEP).

• Nonlinear Functional Analysis and Applications
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• 제27권4호
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• pp.743-756
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• 2022

We obtained results on upper hemi-continuous and pseudo-monotone type two mappings for sets which are not compact. M.S.R. Chowdhury and K.-K. Tan's improved result on Ky Fan's minimax inequality will be used.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.47-56
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• 2024

It is well known that inequalities enable us to analyze and solve complex problems with precision and efficiency. The inequalities provide powerful tools for establishing bounds, optimizing solutions, and deepening our understanding of mathematical concepts, paving the way for advancements in areas such as optimization, analysis, and probability theory. In this paper, we present some properties for Hadamard-Simpsons type inequalities in the classic integral and Riemann-Liouville fractional integral. We use the convexity of the given function and its first derivative.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.113-130
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• 2024

In this work, we explore the existence and uniqueness results for a class of boundary value issues for implicit Volterra-Fredholm nonlinear integro-differential equations (IDEs) with Atangana-Baleanu-Riemann fractional (ABR-fractional) that have non-instantaneous multi-point fractional boundary conditions. The findings are supported by Krasnoselskii's fixed point theorem, Gronwall-Bellman inequality, and the Banach contraction principle. Finally, a demonstrative example is provided to support our key findings.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.197-208
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• 2024

In the present paper, we establish Ulam-Hyres and Ulam-Hyers-Rassias stabilities for nonlinear impulsive integro-differential equations with non-local condition in Banach space. The generalization of Grownwall type inequality is used to obtain our results.

• 대한수학회보
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• 제47권4호
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• pp.777-785
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• 2010

Let X be a linear space and Y be a complete quasi p-norm space. We will show that for each function f : X $\rightarrow$ Y, which satisfies the inequality ${\parallel}{\Delta}_x^nf(y)\;-\;n!f(x){\parallel}\;{\leq}\;\varphi(x,y)$ for suitable control function $\varphi$, there is a unique monomial function M of degree n which is a good approximation for f in such a way that the continuity of $t\;{\mapsto}\;f(tx)$ and $t\;{\mapsto}\;\varphi(tx,\;ty)$ imply the continuity of $t\;{\mapsto}\;M(tx)$.

• Journal of applied mathematics & informatics
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• 제35권3_4호
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• pp.387-397
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• 2017

In order to react the dynamic behavior of the system more actually, it is necessary to solve the first problem of synchronization for Markovian jump complex network system in practical engineering problem. In this paper, the problem of local stochastic synchronization for Markovian nonlinear coupled neural network system is investigated, including nonlinear coupling terms and mode-dependent delays, that is less restriction to other system. By designing the Lyapunov-Krasovskii functional and applying less conservative inequality, we get a new criterion to ensure local synchronization in mean square for Markovian nonlinear coupled neural network system. The criterion introduced some free matrix variables, which are less conservative. The simulation confirmed the validity of the conclusion.

• Kyungpook Mathematical Journal
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• 제55권2호
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• pp.429-438
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• 2015

The objective of this paper is to obtain sharp upper bound for the second Hankel functional associated with the $k^{th}$ root transform $[f(z^k)]^{\frac{1}{k}}$ of normalized analytic function f(z) when it belongs to the class of starlike and convex functions with respect to symmetric points, defined on the open unit disc in the complex plane, using Toeplitz determinants.