• Journal of applied mathematics & informatics
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• 제31권1_2호
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• pp.155-164
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• 2013

In this paper, we have established some common fixed point theorems for two pairs of occasionally weakly compatible hybrid maps sat-isfying a strict contractive condition in a non-archimedean fuzzy metric space. Our result extend, generalized and fuzzify several fixed point theo-rems on metric space.

• Korean Journal of Mathematics
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• 제20권1호
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• pp.33-46
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• 2012

Using the direct method, we prove the Hyers-Ulam stability of the orthogonally additive-quartic functional equation (0.1) $f(2x+y)+f(2x-y)=4f(x+y)+4f(x-y)+10f(x)+14f(-x)-3f(y)-3f(-y)$ for all $x$, $y$ with $x{\perp}y$, in non-Archimedean Banach spaces. Here ${\perp}$ is the orthogonality in the sense of R$\ddot{a}$tz.

• 충청수학회지
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• 제27권2호
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• pp.261-269
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• 2014

In this paper, using fixed point method, we prove the Hyers-Ulam stability of the following functional equation $$(k+1)f(x+y)+f(x+{\sigma}(y))+kf({\sigma}(x)+y)-2(k+1)f(x)-2(k+1)f(y)=0$$ with an involution ${\sigma}$ for a fixed non-zero real number k with $k{\neq}-1$.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제30권4호
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• pp.443-461
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• 2023

In this paper, we establish some common fixed point theorems satisfying contraction mapping principle on partially ordered non-Archimedean fuzzy metric spaces and also derive some coupled fixed point results with the help of established results. We investigate the solution of integral equation and also give an example to show the applicability of our results. These results generalize, improve and fuzzify several well-known results in the recent literature.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제24권2호
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• pp.109-127
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• 2017

In this paper, we solve the following quadratic ${\rho}-functional$ inequalities ${\parallel}f({\frac{x+y+z}{2}})+f({\frac{x-y-z}{2}})+f({\frac{y-x-z}{2}})+f({\frac{z-x-y}{2}})-f(x)-f(y)f(z){\parallel}$ (0.1) ${\leq}{\parallel}{\rho}(f(x+y+z)+f(x-y-z)+f(y-x-z)+f(z-x-y)-4f(x)-4f(y)-4f(z)){\parallel}$, where ${\rho}$ is a fixed non-Archimedean number with ${\mid}{\rho}{\mid}$ < ${\frac{1}{{\mid}4{\mid}}}$, and ${\parallel}f(x+y+z)+f(x-y-z)+f(y-x-z)+f(z-x-y)-4f(x)-4f(y)-4f(z){\parallel}$ (0.2) ${\leq}{\parallel}{\rho}(f({\frac{x+y+z}{2}})+f({\frac{x-y-z}{2}})+f({\frac{y-x-z}{2}})+f({\frac{z-x-y}{2}})-f(x)-f(y)f(z)){\parallel}$, where ${\rho}$ is a fixed non-Archimedean number with ${\mid}{\rho}{\mid}$ < ${\mid}8{\mid}$. Using the direct method, we prove the Hyers-Ulam stability of the quadratic ${\rho}-functional$ inequalities (0.1) and (0.2) in non-Archimedean Banach spaces and prove the Hyers-Ulam stability of quadratic ${\rho}-functional$ equations associated with the quadratic ${\rho}-functional$ inequalities (0.1) and (0.2) in non-Archimedean Banach spaces.

• 대한수학회보
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• 제52권3호
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• pp.789-807
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• 2015

We propose coincidence and common fixed point results for a quadruple of self mappings satisfying common limit range property and weakly compatibility under generalized ${\Phi}$-contractive conditions i Non-Archimedean Menger PM-spaces. As examples we exhibit different types of situations where these conditions can be used. A common fixed point theorem for four finite families of self mappings is presented as an application of the proposed results. The existence and uniqueness of solutions for certain system of functional equations arising in dynamic programming are also presented as another application.

• 충청수학회지
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• 제26권4호
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• pp.887-900
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• 2013

In this paper, we investigate the stability for the functional equation f(3x+y)-3f(2x+y)+3f(x+y)-f(y)=0 in the sense of M. S. Moslehian and Th. M. Rassias.

• 한국수학교육학회지시리즈B:순수및응용수학
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• 제22권4호
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• pp.343-357
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• 2015

Using the fixed point method, we prove the Hyers-Ulam stability of lin- ear mappings in Banach modules over a unital C*-algebra and in non-Archimedean Banach modules over a unital C*-algebra associated with the orthogonally Cauchy- Jensen additive functional equation.

• Korean Journal of Mathematics
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• 제30권2호
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• pp.403-412
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• 2022

In this paper, we introduce the following cubic-quartic functional equation of the form $$f(x+4y)+f(x-4y)=16[f(x+y)+f(x-y)]{\pm}30f(-x)+\frac{5}{2}[f(4y)-64f(y)]$$. Further, we investigate the general solution and the Ulam stability for the above functional equation in non-Archimedean spaces by using the direct method.

• 충청수학회지
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• 제26권2호
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• pp.377-391
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• 2013

The main goal of this paper is to present the additional stability results of the following orthogonally additive and orthogonally quadratic functional equation $$f(\frac{x}{2}+y)+f(\frac{x}{2}-y)+f(\frac{x}{2}+z)+f(\frac{x}{2}-z)=\frac{3}{2}f(x)-\frac{1}{2}f(-x)+f(y)+f(-y)+f(z)+f(-z)$$ for all $x,y,z$ with $x{\bot}y$, which has been introduced in the paper [11], in orthogonality Banach spaces and in non-Archimedean orthogonality Banach spaces.