Showing papers by "Prasanna K. Sahoo published in 2015"
TL;DR: In this article, the authors studied the functional equations of the field of complex numbers, where f(x, y) = 2f(x)f(y) + f(xyz), f(y), x, y, y = 0 in the center Z(G) of the group G. The main goals of this paper are to study the functional equation for all the vertices of the complex numbers.
Abstract: Let G be a group, $${\mathbb{C}}$$
be the field of complex numbers, z
0 be any fixed, nonzero element in the center Z(G) of the group G, and $${\sigma : G \to G}$$
be an involution. The main goals of this paper are to study the functional equations $${f(x{\sigma}yz_{0}) - f(xyz_{0}) = 2f(x)f(y)}$$
and $${f(x{\sigma}yz_{0}) + f(xyz_{0}) = 2f(x)f(y)}$$
for all $${x, y \in G}$$
and some fixed element z
0 in the center Z(G) of the group G.
23 citations
TL;DR: In this article, the Hyers-Ulam stability of the additive-cubic-quartic ACQ (ACQ) functional equation was proved using the direct method and the fixed point method.
Abstract: Using the direct method and the fixed point method, we prove the Hyers-Ulam stability of the following additive-cubic-quartic (ACQ ) functional equation 11[f(x+ 2y) + f(x− 2y)] = 44[f(x+ y) + f(x− y)] + 12f(3y)− 48f(2y) + 60f(y)− 66f(x) in matrix Banach spaces. Furthermore, using the fixed point method, we also prove the Hyers-Ulam stability of the above functional equation in matrix fuzzy normed spaces. c ©2015 All rights reserved.
10 citations
TL;DR: The stitching algorithm gives local and global performance parameters such as link delays over specified time periods so that the network behavior as well as the corresponding local network performance in a mobile network can be derived over a continuous period.
7 citations
TL;DR: The stability of Wilson's functional equations with involution was studied in this paper, where the stability of the Wilson functional equations was shown to be equivalent to the superstability of the functional equations studied by Chung et al. in the spirit of Badora and Ger.
Abstract: Let S be a commutative semigroup, $${\mathbb{C}}$$
the set of complex numbers, $${\mathbb{R}^+}$$
the set of nonnegative real numbers, $${f, g : S \to \mathbb{C}\, \, {\rm and} \, \, \sigma : S \to S}$$
an involution. In this article, we consider the stability of the Wilson’s functional equations with involution, namely $${f(x + y) + f(x + \sigma y) = 2f(x)g(y)}$$
and $${f(x + y) + f(x + \sigma y) = 2g(x)f(y)}$$
for all $${x, y \in S}$$
in the spirit of Badora and Ger (Functional equations—results and advances, pp 3–15, 2002). As consequences of our results, we obtain the superstability of functional equations studied by Chung et al. (J Math Anal Appl 138:208–292, 1989), Chavez and Sahoo (Appl Math Lett 24:344–347, 2011) and Houston and Sahoo (Appl Math Lett 21:974–977, 2008).
6 citations
TL;DR: In this paper, the general solution f : F 2 → S of the equation f ( ϕ ( x, y, u, v ) = f ( x, y ) f ( u, v ) for suitable conditions on the function ϕ : F 4 → F 2, where F will denote either R or C, and S is a multiplicative semigroup.
5 citations
TL;DR: In this article, the stability of two generalizations of the functional equa- tion f(pr,qs)+f(ps,qr ) = f(p,q) f(r,s), namely, f(pl,qs) + g(ps-qr) = h(p/q)h(r/s) for all p,q,r, s ∈ G, where G is a commutative semi-group.
Abstract: This work aims to study of the stability of two generalizations of the functional equa- tion f(pr,qs)+f(ps,qr )= f(p,q) f(r,s), namely (i) f(pr,qs)+g(ps,qr )= h(p,q)h(r,s) ,a nd (ii) f(pr,qs)+g(ps,qr )= h(p,q)k(r,s) for all p,q,r,s ∈ G ,w hereG is a commutative semi- group. Thus this work is a continuation of our earlier works (15 )a nd (16), and the functional equations studied here arise in the characterizations of symmetrically compositive sum form distance measures.
1 citations
TL;DR: In this article, the Levi-Civita functional inequality was studied in the field of complex numbers and the Hyers-Ulam stability problem of the functional inequalities was solved.
Abstract: Let $G$
be a commutative group and $\mathbb{C}$
the field of complex numbers, $\mathbb{R}^{+}$
the set of positive real numbers and $f,g,h,k:G\times \mathbb{R}^{+}\rightarrow \mathbb{C}$
. In this paper, we first consider the Levi-Civita functional inequality $$\begin{eqnarray}\displaystyle |f(x+y,t+s)-g(x,t)h(y,s)-k(y,s)|\leq {\rm\Phi}(t,s),\quad x,y\in G,t,s>0, & & \displaystyle
onumber\end{eqnarray}$$
where ${\rm\Phi}:\mathbb{R}^{+}\times \mathbb{R}^{+}\rightarrow \mathbb{R}^{+}$
is a symmetric decreasing function in the sense that ${\rm\Phi}(t_{2},s_{2})\leq {\rm\Phi}(t_{1},s_{1})$
for all $0
1 citations
TL;DR: In this article, the stability of the functional equation related to inner product spaces has been studied using the fixed point method, and the stability has been shown to be robust to the assumption that the inner product space is a fuzzy Banach space.
Abstract: Using the fixed point method, we prove some results concerning the stability of the functional equation \begin{eqnarray*} \sum^{2n}_{i=1}f(x_{i}-\frac{1}{2n}\sum^{2n}_{j=1}x_{j})=\sum^{2n}_{i=1}f(x_{i})-2n f(\frac{1}{2n}\sum^{2n}_{i=1}x_{i}) \end{eqnarray*} where $f$ is defined on a vector space and taking values in a fuzzy Banach space, which is said to be a functional equation related to a characterization of inner product spaces.
TL;DR: In this article, the authors aim to determine all functions that satisfy the functional equation f(pr, qs) + g(ps, qr) = h(p,q) + k(r,s) for all p, q, r, s ∈ G, where G is a group and \({\mathbb{C}}\) is the field of complex numbers.
Abstract: This work aims to determine all functions \({f, g, h, k : G \to \mathbb{C}}\) that satisfy the functional equation f(pr, qs) + g(ps, qr) = h(p,q) + k(r,s) for all p, q, r, s ∈G, where G is a group and \({\mathbb{C}}\) is the field of complex numbers.