• 충청수학회지
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• 제32권1호
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• pp.29-46
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• 2019

We introduce a generalized cubic functional equation and investigate the Hyers-Ulam stability of the cubic functions as solutions to the generalized cubic functional equation on a quasi-fuzzy anti-${\beta}$-Banach space by both the direct method and the fixed point method.

• Journal of the Korean Society for Industrial and Applied Mathematics
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• 제25권1호
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• pp.16-25
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• 2021

This paper is studied the existence of a solution for the impulsive Cauchy problem involving the Caputo fractional derivative in Banach space by using topological structures. We based on using topological degree method and fixed point theorem with some suitable conditions. Further, some topological properties for the set of solutions are considered. Finally, an example is presented to demonstrate our results.

• Nonlinear Functional Analysis and Applications
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• 제26권4호
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• pp.793-809
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• 2021

This paper gives sufficient conditions to ensure the existence and stability of solutions for generalized nonlinear fractional integrodifferential equations of order α (1 < α < 2). The main theorem asserts the stability results in a weighted Banach space, employing the Krasnoselskii's fixed point technique and the existence of at least one mild solution satisfying the asymptotic stability condition. Two examples are provided to illustrate the theory.

• 대한수학회논문집
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• 제37권3호
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• pp.801-812
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• 2022

In this paper, we introduce the multi-derivations on rings and present some examples of such derivations. Then, we unify the system of functional equations defining a multi-derivation to a single formula. Applying a fixed point theorem, we will establish the generalized Hyers-Ulam stability of multi-derivations in Banach module whose upper bounds are controlled by a general function. Moreover, we give some important applications of this result to obtain the known stability outcomes.

• Korean Journal of Mathematics
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• 제30권4호
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• pp.561-569
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• 2022

In this paper, we study the generalization of the Banach contraction principle in the vector space, involving four rational square terms in the inequality, by using the notation of bilinear functional. We also present an extension of Selberg's inequality to vector space.

• Nonlinear Functional Analysis and Applications
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• 제28권3호
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• pp.851-863
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• 2023

We study the appropriate conditions for the findings of uniqueness and existence for a group of boundary value problems for impulsive Ψ-Caputo fractional nonlinear Volterra-Fredholm integro-differential equations (V-FIDEs) with symmetric boundary non-instantaneous conditions in this paper. The findings are based on the fixed point theorem of Krasnoselskii and the Banach contraction principle. Finally, the application is provided to validate our primary findings.

• Nonlinear Functional Analysis and Applications
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• 제29권1호
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• pp.165-177
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• 2024

In this paper, we investigate the suitable conditions for the existence results for a class of 𝔍-Hilfer fractional nonlinear Fredholm-Volterra models with new conditions. The findings are based on Banach contraction principle and Schauder's fixed point theorem. Also, the generalized Hyers-Ulam stability and generalized Hyers-Ulam-Rassias stability for solutions of the given problem are provided.

• 대한수학회보
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• 제42권4호
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• pp.661-670
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• 2005

In this paper, we deal with approximations of com­mon fixed points of the iterative sequences with errors for three asymptotically nonexpansive mappings in a uniformly convex Banach space. Our results generalize and improve the corresponding results of Khan and Takahashi, Schu, Takahashi and Tamura, and others.

• East Asian mathematical journal
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• 제26권3호
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• pp.429-440
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• 2010

In this paper, we study a new one-step iterative scheme with error for approximating common fixed points of non-self asymptotically nonexpansive in the intermediate sense mappings in uniformly convex Banach spaces. Also we have proved weak and strong convergence theorems for above said scheme. The results obtained in this paper extend and improve the recent ones, announced by Zhou et al. [27] and many others.

• Kyungpook Mathematical Journal
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• 제49권4호
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• pp.701-712
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• 2009

In this paper, we first introduce a family S = {$S_n$ : C ${\rightarrow}$ C} of non-Lipschitzian mappings, called total asymptotically nonexpansive (briefly, TAN) on a nonempty closed convex subset C of a real Banach space X, and next give necessary and sufficient conditions for strong convergence of the sequence {$x_n$} defined recursively by the algorithm $x_{n+1}$ = $S_nx_n$, $n{\geq}1$, starting from an initial guess $x_1{\in}C$, to a common fixed point for such a continuous TAN family S in Banach spaces. Finally, some applications to a finite family of TAN self mappings are also added.