Ravi Krishnan

Sacred Heart College · Department of Mathematics

In this study, we achieve the general solution and investigate Ulam-Hyers stabilities involving a general control function, sum of powers of norms, product of powers of norms and mixed product-sum of powers of norms of the duodecic functional equation in quasi-β-normed spaces via fixed point method. We also illustrate a counter-example for non-stab...

In this paper, we acquire the general solution of the undecic functional equation f(x + 6y) - 11f(x + 5y) + 55f(x + 4y) - 165f(x + 3y) + 330f(x + 2y) - 462f(x + y) + 462f(x) - 330f(x - y) + 165f(x - 2y) - 55f(x - 3y) + 11f(x - 4y) - f(x - 5y) = 39916800f(y). We also obtain the generalized Ulam-Hyers stability of the above functional equation in qua...

This paper suggests one possible method to model additive type of functional equations using eigenvalues and eigenvectors of matrices with suitable numerical examples. The authors have defined a new type of Row Sum Matrix(RSM) and have discussed its eigenvalues and eigenvectors in order to model functional equations. The famous additive cauchy func...

In this paper, the general solution and generalized Ulam-Hyers stability of a reciprocal type functional equation and obtained in quasi-beta-normed spaces.

In this paper, we obtain the general solution and the generalized Ulam-Hyers stability of the 2-variable $k$-AC mixed type functional equation$$\begin{aligned}& f(x+k y, z+k w)+f(x-k y, z-k w) \\& \quad=k^2[f(x+y, z+w)+f(x-y, z-w)]+2\left(1-k^2\right) f(x, z) .\end{aligned}$$for any $k \in Z-\{0, \pm 1\}$ in $\alpha$-Šerstnev Menger Probabilistic n...

In this paper, we introduce a new generalized reciprocal functional equation and study its Hyers-Ulam-Rassias stability. We also provide the counter examples for some cases, Ulam-Găvruta-Rassias stability and Hyers-Ulam-Rassias stability in non-Archimedean fields.

In this paper, we obtain the general solution of the decic functional equation (Equation presented) We also investigate the generalized Hyers-Ulam stability of decic functional equation in quasi-β-normed spaces using fixed point method.

In this paper, we introduce the following quattuordecic functional equation f(x+7y)-14f(x+6y)+91f(x+5y)-364f(x+4y)+1001f(x+3y)-2002f(x+2y)+3003f(x+y)-3432f(x)+3003f(x-y)-2002f(x-2y)+1001f(x-3y)-364f(x-4y)+91f(x-5y)-14f(x-6y)+f(x-7y)=14!f(y), investigate the general solution and prove the stability of this quattuordecic functional equation in quasi...

In this paper, we obtain the general solution and investigate the generalized Hyers-Ulam stability of a new quadratic functional equation f (3x+ y)+ f (2x+ y)+5 f (x- y) = 18 f (x)+7 f (y) in quasi-β-normed spaces using fixed point method. A counter-example is also presented for a singular case. 2000 Mathematics Subject Classification.: 39B82, 39B7...

In this paper, we introduce a new quadratic functional equation, obtain the general solution and investigate the Hyers-Ulam stability, Hyers-Ulam-Rassias stability and generalized Hyers-Ulam-Rassias stability for the quadratic functional equations in Felbin’s type fuzzy normed linear spaces. A counter-example for singular case is also provided in t...

In this paper, we investigate the general solution and Hyers–Ulam–Rassias stability of a new mixed type of additive and quintic functional equation of the form f ( 3 x + y ) − 5 f ( 2 x + y ) + f ( 2 x − y ) + 10 f ( x + y ) − 5 f ( x − y ) = 10 f ( y ) + 4 f ( 2 x ) − 8 f ( x ) $$f\left( {3x + y} \right) - 5f\left( {2x + y} \right) + f\left( {2x -...

In this paper, we obtain the solution of a new generalized reciprocal type functional equation in two variables and investigate its generalized Hyers–Ulam stability in non-Archimedean fields. We also present the pertinent stability results of Hyers–Ulam–Rassias stability, Ulam–Gavruta–Rassias stability and J. M. Rassias stability controlled by the...

In this paper, the authors obtain the general solution and the generalized Hyers-Ulam-Rassias stabilities of the following new general $k$-cubic functional equation in Banach spaces \begin{eqnarray*} kf(x+ky)-f(kx+y) &=&\frac{1}{2}(k^{3}-k)[f(x+y)+f(x-y)]+(k^{4}-1)f(y) \\ &&-2(k^{3}-k)f(x) \end{eqnarray*} for any real $k\in \mathbb{R}-\left\{0,\pm1...

In this paper, we derive general solution of new-dimensional quintic and sextic functional equations and investigate the Hyers–Ulam stability, Hyers–Ulam–Rassias stability and generalized Hyers–Ulam– Rassias stability for quintic and sextic functional equations in Felbin type fuzzy normed linear spaces. Also, we give the counter examples for the Hy...

In this paper, we obtain the generalized Hyers-Ulam stability of a the functional equation f(2x + y) + f(x + 2y) - 9f(x + y) + f(x - y) = f(2x) - 7f(x) + 8f(-y) + f(y).

In this paper, we obtain the general solution and investigate the generalized Hyers-Ulam stability of a reciprocal type functional equation in several variables of the form ∏ i=2 m r(x 1 +x i ) ∑ i=2 m ∏ j=2,j≠i m r(x 1 +x j )=∏ i=1 m r(x i ) ∑ i=2 m r(x 1 )∏ j=2,j≠i m r(x j )+(m-1)∏ i=2 m r(x i ), where m is a positive integer with m≥3.

In this paper, the authors introduce a new generalized radical reciprocal quadratic functional equation of the form f(√ x2+y2/n) ± mf (√x2+y2)=(n2±m) f(x)f(y)/ f(x)+f(y) and investigate its generalized Hyers-Ulam stability in Felbin's type fuzzy normed linear spaces. Also we give counter example for the Hyers-Ulam-Rassias stability of the radical r...

In this paper, the reciprocal difference functional equation (or RDF equation) and the reciprocal adjoint functional equation (or RAF equation) are introduced. Then the pertinent Ulam stability problem for these functional equations is solved, together with the extended Ulam (or Rassias) stability problem and the generalized Ulam (or Ulam-Gavruta-R...

In this paper, we investigate the generalized Hyers-Ulam stability of Reciprocal Difference and Adjoint Functional equations by applying fixed point method.

In this paper, the authors investigate the general solution and Ulam stability of mixed type cubic and additive functional equation of the form introduced by the first author. We also investigate the first author's stability of the equation (*) controlled by a mixed type product - sum of powers of norms.

In this paper, the authors study the general solution and stability of a cubic functional equation f (2x + y) - 3 f (x + y) + f (x - y) = 6f(x)-3f(y) in Menger probabilistic normed spaces.

We obtain the general solution and investigate the generalized Hyers-Ulam stability of the new generalized mixed type additive and quadratic functional equation in fuzzy normed space.

We obtain the general solution and investigate the Hyers-Ulam-Rassias stability of the functional equation f(ax-y)±af(x±y)=(a±1)[af(x)±f(y)] in non-Archimedean -fuzzy normed spaces.

In this paper, the authors investigate the general solution of a new cubic functional equation 3f (x + 3y) − f (3x + y) = 12[f (x + y) + f (x − y)] + 80f (y) − 48f (x) and discuss its generalized Hyers-Ulam-Rassias stability in Banach spaces and stability in fuzzy normed spaces.

In this paper, the authors investigate the general solution of a new cubic functional equation 3f (x + 3y) − f (3x + y) = 12[f (x + y) + f (x − y)] + 80f (y) − 48f (x) and discuss its generalized Hyers-Ulam-Rassias stability in Banach spaces and stability in fuzzy normed spaces.

The Ulam-Gavruta-Rassias (UGR) stability involving a product of powers of norms was established by J.M. Rassias in 1982-1989 and employed by B. Bouikhalene, E. Elquorachi,. Nakmahachalasint, B.V. Senthil Kumar, K.Ravi and M. Arunkumar in 2007-08. Further, UGR stability for Rassias Reciprocal functional equation was investigated by K. Ravi and B.V....

The authors investigate the general solution and the generalized Hyers-Ulam stability of a 2-variable cubic functional equation of the form f(2x+y,2u+v)+f(2x-y,2u-v)=2f(x+y,u+v)+2f(x-y,u-v)+12f(x,u)·

Interferon-gamma (IFN-gamma) is a proinflammatory cytokine that induces the proliferation of T-helper 1 cells that contribute to allograft rejection. Surprisingly, allografts transplanted in IFN-gamma deficient mice are rapidly rejected, suggesting that this cytokine has a paradoxical role in regulating alloimmune responses. Since dendritic cells (...

In this paper, we discuss the Hyers-Ulam stability, Ulam-Gavruta-Rassias stability, the extended Ulam stability and Refined Ulam stability problems for the Generalized Reciprocal Functional equation (or GRF equation) in several variables.

We obtain the general solution of a new quadratic functional equation: 3f(2x+y)+3f(x+2y)-10f(x+y)+2f(x-y)=7f(x)+7f(y) and investigate its stability in a fuzzy normed space and also using the fixed point method.

In this paper, we introduce and investigate the general solution of a new cubic and additive functional equation 3f(x+y+z) + f(-x+y+z) + f(x-y+z) + f(x+y-z)+4[f(x) + f(y) + f(z)] = 4[f(x + y) + f(x + z) + f(y + z)] and discuss its Hyers-Ulam-Rassias and J.M. Rassias stability in quasi-Banach spaces.

In this paper, we obtain the general solution and the generalized Hyers-Ulam-Rassias stability of the generalized mixed type of functional equation, for fixed integers a with a ≠ 0,±1.

Dendritic cells (DC) mediate potent alloimmune responses through the positive costimulatory molecules CD40, CD80 and CD86 while the negative costimulatory molecules, immunoglobulin-like transcript 2 (ILT2), ILT3 and ILT4 have been associated with tolerogenic DC function. Due to the pivotal role played by DC in immunity the effect of the immunosuppr...

In this paper we prove the Hyers-Ulam-Rassias stability of homomorphisms in real Banach algebras for the generalized Cauchy-Jensen functional equation.

In this paper, we investigate the generalized Hyers - Ulam - Rassias stability of a new quadratic functional equation f(2x + y) + f(2x y) = 2f(x + y) + 2f(x y) + 4f(x) 2f(y):

We obtain the general solution and the generalized Hyers-Ulam-Rassias stability of the quartic functional equation f(x+2y)+f(x-2y)=2f(x)+32f(y)+48f(xy) for all x,y∈ℝ with the help of Fréchet functional equation.

In this paper, we investigate the Hyers-Ulam stability for a new quartic functional equation fx+y 2+z+fx+y 2-z+fx-y 2+z+fx-y 2-z+f(x)+f(y)-2f(z)==1 8{f(x+y)+f(x-y)+4[f(y+z)+f(y-z)+f(x+z)+f(x-z)]} in non-archimedean normed space.

Ww establish the general solution of the functional equation f(x+3y)+f(x-3y)+16f(x)=9f(x+y)+9f(x-y) for all x,y,∈ℝ without assuming any regularity conditions on the unknown function f. In solving this functional equation we exploit an important result due to M. Hosszú [Bul. Inst. Politeh. Iaşi, N. Ser. 10(14), No. 1–2, 27–28 (1964; Zbl 0197.12302)]...

We obtain the general solution and the generalized Hyers-Ulam stability of the quadratic functional equation f(3x+y)+f(3x-y)=f(x+y)+f(x-y)+16f(x).

Cytotoxic T-lymphocyte antigen 4 immunoglobulin (CTLA4-Ig) and interleukin (IL)-10 are immunomodulatory molecules which target CD28 costimulation by acting either directly or indirectly on the CD80/86 receptors on dendritic cells (DCs). This study examined the effect of combined treatment with CTLA4-Ig and IL-10 on T-cell responsiveness in a dendri...

Immunological rejection is the major cause of human corneal allograft failure. We hypothesized that local production of IL-4 or the p40 subunit of IL-12 (p40 IL-12) by the grafted cornea might prolong allograft survival. Replication-deficient adenoviral vectors encoding ovine IL-4 or p40 IL-12 and GFP were generated and used to infect ovine corneas...

CTLA4 (CD152) is a transmembrane molecule expressed on activated T cells and functions as a negative regulator of T cell activation upon binding to the costimulatory molecules CD80/86. In this study, CTLA4eEGFP constructs were engineered by cloning the extracellular domains of ovine and human CTLA4 (CTLA4e) 'in frame' with the enhanced green fluore...

The CD40 molecule is a member of the tumour necrosis factor receptor (TNFR)-like supergene family and plays a major role as a co-stimulatory molecule in the activation of T cells in response to antigens presented by dendritic cells. In this study, reverse transcription-PCR cloning was used to derive the sequence encoding ovine CD40. The ovine CD40...

Dendritic cells (CD) are professional antigen-presenting cells of the immune system that play a central role in the initiation of the alloimmune response. Recently these cells have been found to also play a role in the maintenance of peripheral tolerance to antigens. Dendritic cells initiate alloimmunity by migrating from the graft to lymphoid site...

Human myeloid DC were generated from peripheral blood mononuclear cells by monocyte adhesion and subsequent culture with rhGM-CSF and rhIL-4. We transduced immature (day 5 of culture) myeloid DC with an E1-deleted replication-deficient adenoviral vector encoding the cytokine IL-10 (AdV IL-10) and a control adenovirus MX-17 (AdV MX 17). Human DC tra...

The authors consider second-order difference equations of the type where α > 0 is the ratio of odd positive integers, {qn} is a positive sequence, and {σ(n)} is a positive increasing sequence of integers with σ(n) → ∞ as n → ∞. They give some oscillation and comparison results for equation (E).

The authors consider difference equations of the form where an > 0, qn > 0, f, and φ are continuous real valued functions, and uf(u) > 0 for u ≠ 0. They give oscillation results for equation (E). Examples are included to illustrate the results.

Modification of a donor cornea by gene therapy ex vivo has potential to modulate irreversible rejection, the major cause of corneal graft failure. Our aim was to transfer the gene encoding mammalian IL-10 to ovine donor corneas and to determine subsequent orthotopic corneal allograft survival in an outbred sheep model. The replicative capacity of o...

The asymptotic and oscillatory behavior of solutions of Volterra summation equations y n =p n ±∑ s=0 n-1 K(n,s)f(s,y s ),n∈ℕ where ℕ={0,1,2,⋯}, are studied. Examples are included to illustrate the results.

Interleukin 12 (IL-12) is a heterodimeric cytokine composed of two subunits that form the biologically active p70 molecule, and is a potent inducer of the pro-inflammatory cytokine IFN-gamma. In this study the coding sequence for ovine interleukin 12 p35 and p40 subunits was derived by RT-PCR cloning. Ovine p35 and p40 cDNA sequences show a high le...

Some new oscillation criteria are obtained for the second-order half-linear difference equation where α 0 is a ratio of odd positive integers. The method uses techniques based on a Riccati type difference inequality. Examples are inserted to illustrate the results.

The paper contains sufficient conditions under which all solutions of nonlinear functional equations are oscillatory.

The authors consider the quasilinear difference equation δ(pn−1(δyn−1)α)=qnyβn+rnand obtain results on the asymptotic behavior of solutions of (∗) including sufficient conditions for all solutions to be bounded or unbounded. Some results on the existence and behavior of nonincreasing solutions of (∗) are also obtained. Examples are inserted to illu...

Orthotopic penetrating keratoplasty in the sheep was developed as an outbred preclinical model to allow correlation of the cellular infiltrate during graft rejection with local production of cytokine mRNA. Penetrating corneal autografts and allografts were performed in Merino sheep. Graft outcome was followed at the slit-lamp. Corneal infiltrates w...

This study investigates the therapeutic efficacy of an anti-vascular cell adhesion molecule (VCAM)-1 monoclonal antibody (mAb), alone or in combination with an anti-leukocyte function-associated-1 mAb, in prolonging allograft survival in an ovine model of renal transplantation. The kinetics of VCAM-1 induction and expression during renal allograft...

This paper reports the production and characterization of three monoclonal antibodies (mAb) recognizing ovine vascular cell adhesion molecule-1 (VCAM-1). The mAb were raised against sheep umbilical vein endothelial cells (ShUVEC) and flow cytometric analysis demonstrated that one mAb, QE4G9, was cross-reactive with human VCAM-1 expressed on Chinese...

This paper reports the isolation and characterization of sheep umbilical vein endothelial cells (ShUVEC) and examines the kinetics of the expression of intercellular cell adhesion molecule-1 (ICAM-1) and vascular cell adhesion molecule-1 (VCAM-1). In culture, the cells demonstrate the classical endothelial cell phenotype, including the expression o...

The purpose of this paper is to highlight the work of an extraordinary mathematician Leonhard Paul Euler and thereby motivate the mathematics lovers to go through his works.