Gwang Hui Kim

Common fixed point theorems for (ψ, φ)-weak nonlinear contraction in partially ordered sets

The purpose of this article is to present some fixed point theorems for (ψ, φ)-weak contractive mappings in a complete metric space endowed with a partial order. As an application of the main result, we give an existence theorem for the solution of a periodic boundary value problem.2000 Mathematics Subject Classification: 47H10.

Nearly Radical Quadratic Functional Equations in p-2-Normed Spaces

We establish some stability results in 2-normed spaces for the radical quadratic functional equation 𝑓(∑𝑛𝑖=1(𝑥𝑖

Solution and Hyers-Ulam-Rassias Stability of Generalized Mixed Type Additive-Quadratic Functional Equations in Fuzzy Banach Spaces

By using fixed point methods and direct method, we establish the generalized Hyers-Ulam stability of the following additive-quadratic functional equation for fixed integers with in fuzzy Banach spaces.

A Fixed Point Theorem for Contraction Type Maps in Partially Ordered Metric Spaces and Application to Ordinary Differential Equations

We present a fixed point theorem for generalized contraction in partially ordered complete metric spaces. As an application, we give an existence and uniqueness for the solution of a periodic boundary value problem.

Pata contractions and coupled type fixed points

AbstractA new coupled fixed point theorem related to the Pata contraction for mappings having the mixed monotone property in partially ordered complete metric spaces is established. It is shown that the coupled fixed point can be unique under some extra suitable conditions involving mid point lower or upper bound properties. Also the corresponding convergence rate is estimated when the iterates of our function converge to its coupled fixed point. MSC:47H10, 34B15, 54H25.

Bounded Approximate Identities in Ternary Banach Algebras

Let A be a ternary Banach algebra. We prove that if A has a left-bounded approximating set, then A has a left-bounded approximate identity. Moreover, we show that if A has bounded left and right approximate identities, then A has a bounded approximate identity. Hence, we prove Altman’s Theorem and Dixon’s Theorem for ternary Banach algebras.

Nearly Derivations on Banach Algebras

Let 𝑛 be a fixed integer greater than 3 and let 𝜆 be a real number with 𝜆 ≠ ( 𝑛 2 − 𝑛 + 4 ) / 2 . We investigate the Hyers-Ulam stability of derivations on Banach algebras related to the following generalized Cauchy functional inequality ‖ ∑ 1 ≤ 𝑖 𝑗 ≤ 𝑛 1 ≤ 𝑘 𝑙 ≠ 𝑖 , 𝑗 ≤ 𝑛 𝑓 ( ( 𝑥 𝑖 + 𝑥 𝑗 ∑ ) / 2 + 𝑛 − 2 𝑙 = 1 𝑥 𝑘 𝑙 ∑ ) + 𝑓 ( 𝑛 𝑖 = 2 𝑥 𝑖 ) + 𝑓 ( 𝑥 1 ∑ ) ‖ ≤ ‖ 𝜆 𝑓 ( 𝑛 𝑖 = 1 𝑥 𝑖 ) ‖ .

Approximate -Lie Homomorphisms and Jordan -Lie Homomorphisms on -Lie Algebras

Using fixed point methods, we establish the stability of 𝑛-Lie homomorphisms and Jordan 𝑛-Lie homomorphisms on 𝑛-Lie algebras associated to the following generalized Jensen functional equation ∑𝜇𝑓(𝑛𝑖=1𝑥𝑖∑/𝑛)

Generalized Hyers-Ulam Stability of the Second-Order Linear Differential Equations

We prove the generalized Hyers-Ulam stability of the 2nd-order linear differential equation of the form 𝑦

Nearly Quadratic Mappings over -Adic Fields

We establish some stability results over -adic fields for the generalized quadratic functional equation where and .