The “oldest quartic” functional equation was introduced and solved by the author of this paper (s... more The “oldest quartic” functional equation was introduced and solved by the author of this paper (see: Glas. Mat. Ser. III 34 (54) (1999), no. 2, 243-252) which is of the form: f(x + 2y) + f(x − 2y) = 4[f(x + y) + f(x − y)] − 6f(x)+ 24f(y). Interesting results have been achieved by S.A. Mohiuddine et al., since 2009. In this paper, we are introducing new quartic functional equations, and establish fundamental formulas for the general solution of such functional equations and for “Ulam stability” of pertinent quartic functional inequalities.
In 1940 S. M. Ulam proposed at the University of Wisconsin the problem: “Give conditions in order... more In 1940 S. M. Ulam proposed at the University of Wisconsin the problem: “Give conditions in order for a linear mapping near an approximately linear mapping to exist”. In 1982-2013, the second author solved the above Ulam problem for a variety of quadratic mappings. Interesting stability results have been achieved by S. A. Mohiuddine et al., since 2009. In this paper, we solve the Ulam stability problem for Euler-Lagrange (α, β; k) quadratic mapping. The other authors of this research area have established important results also on functional inequalities.
One of the generalizations of statistical convergence is I-convergence which was introduced by Ko... more One of the generalizations of statistical convergence is I-convergence which was introduced by Kostyrko et al.[12]. In this paper, we define and study the concept of I-convergence, I*-convergence, I-limit points and I-cluster points of double sequences in probabilistic normed space. We discuss the relationship between I2-convergence and I* 2-convergence, ie, we show that I* 2-convergence implies I2-convergence in probabilistic normed space.
The main purpose of this paper is to characterize the classes of matrices (ces [(p),(q)], cσ) and... more The main purpose of this paper is to characterize the classes of matrices (ces [(p),(q)], cσ) and (ces [(p),(q)], l∞ σ), where cσ is the space of all bounded sequences all of whose σ-means are equal, l∞ σ is the space of σ-bounded sequences, and ces [(p),(q)] is the generalized Cesàro sequence space.
Abstract In this article, we prove a Korovkin type approximation theorem for a function of two va... more Abstract In this article, we prove a Korovkin type approximation theorem for a function of two variables by using the notion of statistical A-summability. We also study the rate of statistical A-summability of positive linear operators. Finally we construct an example by Bleimann et al. operators to show that our result is stronger than those of previously proved by other authors.
Información del artículo Almost bounded variation of double sequences and some four dimensional s... more Información del artículo Almost bounded variation of double sequences and some four dimensional summability matrices.
The “oldest quartic” functional equation was introduced and solved by the author of this paper (s... more The “oldest quartic” functional equation was introduced and solved by the author of this paper (see: Glas. Mat. Ser. III 34 (54) (1999), no. 2, 243-252) which is of the form: f(x + 2y) + f(x − 2y) = 4[f(x + y) + f(x − y)] − 6f(x)+ 24f(y). Interesting results have been achieved by S.A. Mohiuddine et al., since 2009. In this paper, we are introducing new quartic functional equations, and establish fundamental formulas for the general solution of such functional equations and for “Ulam stability” of pertinent quartic functional inequalities.
In 1940 S. M. Ulam proposed at the University of Wisconsin the problem: “Give conditions in order... more In 1940 S. M. Ulam proposed at the University of Wisconsin the problem: “Give conditions in order for a linear mapping near an approximately linear mapping to exist”. In 1982-2013, the second author solved the above Ulam problem for a variety of quadratic mappings. Interesting stability results have been achieved by S. A. Mohiuddine et al., since 2009. In this paper, we solve the Ulam stability problem for Euler-Lagrange (α, β; k) quadratic mapping. The other authors of this research area have established important results also on functional inequalities.
One of the generalizations of statistical convergence is I-convergence which was introduced by Ko... more One of the generalizations of statistical convergence is I-convergence which was introduced by Kostyrko et al.[12]. In this paper, we define and study the concept of I-convergence, I*-convergence, I-limit points and I-cluster points of double sequences in probabilistic normed space. We discuss the relationship between I2-convergence and I* 2-convergence, ie, we show that I* 2-convergence implies I2-convergence in probabilistic normed space.
The main purpose of this paper is to characterize the classes of matrices (ces [(p),(q)], cσ) and... more The main purpose of this paper is to characterize the classes of matrices (ces [(p),(q)], cσ) and (ces [(p),(q)], l∞ σ), where cσ is the space of all bounded sequences all of whose σ-means are equal, l∞ σ is the space of σ-bounded sequences, and ces [(p),(q)] is the generalized Cesàro sequence space.
Abstract In this article, we prove a Korovkin type approximation theorem for a function of two va... more Abstract In this article, we prove a Korovkin type approximation theorem for a function of two variables by using the notion of statistical A-summability. We also study the rate of statistical A-summability of positive linear operators. Finally we construct an example by Bleimann et al. operators to show that our result is stronger than those of previously proved by other authors.
Información del artículo Almost bounded variation of double sequences and some four dimensional s... more Información del artículo Almost bounded variation of double sequences and some four dimensional summability matrices.
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Papers by S.A. Mohiuddine
Mat. Ser. III 34 (54) (1999), no. 2, 243-252) which is of the form:
f(x + 2y) + f(x − 2y) = 4[f(x + y) + f(x − y)] − 6f(x)+ 24f(y).
Interesting results have been achieved by S.A. Mohiuddine et al., since 2009. In this paper, we are introducing new quartic
functional equations, and establish fundamental formulas for the general solution of such functional equations and for “Ulam stability” of pertinent quartic functional inequalities.
mapping near an approximately linear mapping to exist”. In 1982-2013, the second author solved the above Ulam problem
for a variety of quadratic mappings. Interesting stability results have been achieved by S. A. Mohiuddine et al., since 2009. In this paper, we solve the Ulam stability problem for Euler-Lagrange (α, β; k) quadratic mapping. The other authors of
this research area have established important results also on functional inequalities.
Mat. Ser. III 34 (54) (1999), no. 2, 243-252) which is of the form:
f(x + 2y) + f(x − 2y) = 4[f(x + y) + f(x − y)] − 6f(x)+ 24f(y).
Interesting results have been achieved by S.A. Mohiuddine et al., since 2009. In this paper, we are introducing new quartic
functional equations, and establish fundamental formulas for the general solution of such functional equations and for “Ulam stability” of pertinent quartic functional inequalities.
mapping near an approximately linear mapping to exist”. In 1982-2013, the second author solved the above Ulam problem
for a variety of quadratic mappings. Interesting stability results have been achieved by S. A. Mohiuddine et al., since 2009. In this paper, we solve the Ulam stability problem for Euler-Lagrange (α, β; k) quadratic mapping. The other authors of
this research area have established important results also on functional inequalities.