Erdal Gül
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View article: Hermite-Hadamard Inequalities for a New Class of Generalized-(s,m) via Fractional Integral
Hermite-Hadamard Inequalities for a New Class of Generalized-(s,m) via Fractional Integral Open
This paper defines a new generalized (s,m)-σ convex function using the σ convex functions and provides some applications and exact results for this kind of functions. The new definition of the (s,m)-σ convex function class is used to obtai…
View article: Qualitative analysis of evolution equations: Weakly continuous semigroups in banach spaces
Qualitative analysis of evolution equations: Weakly continuous semigroups in banach spaces Open
Evolution equations and operator semigroups in Banach spaces play a pivotal role across various branches of applied mathematics. This paper focuses on the qualitative analysis of evolution equations, particularly first-order linear partial…
View article: Some integral inequalities through tempered fractional integral operator
Some integral inequalities through tempered fractional integral operator Open
In this article, we adopt the tempered fractional integral operators to develop some novel Minkowski and Hermite-Hadamard type integral inequalities. Thus, we give several special cases of the integral inequalities for tempered fractional …
View article: Some novel estimations of hadamard type inequalities for different kinds of convex functions via tempered fractional integral operator
Some novel estimations of hadamard type inequalities for different kinds of convex functions via tempered fractional integral operator Open
In this article, Hermite-Hadamard type inequalities for (h, m)-convex and s-convex functions are established by using tempered fractional integral operators. Also, some integral inequalities related to the right and left sides of the Hermi…
View article: On Minkowski Inequalities Involving Fractional Calculus With General Analytic Kernels
On Minkowski Inequalities Involving Fractional Calculus With General Analytic Kernels Open
There have been many proposed forms of fractional calculus, which can be grouped into a few broad classes of operators. By replacing the kernel of the power function with another kernel function, the traditional Riemann-Liouville formula a…
View article: Some novel estimations of hadamard type inequalities for different kinds of convex functions via tempered fractional integral operator
Some novel estimations of hadamard type inequalities for different kinds of convex functions via tempered fractional integral operator Open
In this article, the hermite hadamard inequality for (h,m)-convex and s-convex functions is established by using tempered fractional integrals. And some integral inequalities related to the right and left inequality of the hermit hadamard …
View article: Almost a Hilbert Space
Almost a Hilbert Space Open
Kuelbs \cite{K} has shown that every infinite-dimensional separable Banach space $\mathcal{B}$ can always be densely and continuously embedded in a separable Hilbert space $\mathcal{H}$. If $\mathcal{L}[\mathcal{B}]$ is the set bounded lin…
View article: On the regularized trace of a differential operator of Sturm-Liouville type
On the regularized trace of a differential operator of Sturm-Liouville type Open
In this work, we study a spectral problem for the abstract Sturm-Liouville operator with a bounded operator coefficient V(t) and with periodic boundary conditions on the interval [0, ?], and we present a regularized trace formula for this …
View article: On a regularized trace formula
On a regularized trace formula Open
In this paper, we study the spectral properties of a self-adjoint differential operator with bounded operator-valued coefficient defined on a separable Hilbert space and derive a regularized trace formula for this operator.
View article: A Second Regularized Trace Formula for a Fourth Order Differential Operator
A Second Regularized Trace Formula for a Fourth Order Differential Operator Open
In applications, many states given for a system can be expressed by orthonormal elements, called “state elements”, taken in a separable Hilbert space (called “state space”). The exact nature of the Hilbert space depends on the system; for …
View article: Abel extensions of some classical Tauberian theorems
Abel extensions of some classical Tauberian theorems Open
The well-known classical Tauberian theorems given for Aλ (the discrete Abel mean) by Armitage and Maddox in [Armitage, H. D and Maddox, J. I., Discrete Abel means, Analysis, 10 (1990), 177–186] is generalized. Similarly the ”one-sided” Tau…
View article: Tauberian theorems for statistical convergence
Tauberian theorems for statistical convergence Open
The Tauberian theorems for statistical limitable method are proved by both Fridy and Khan \cite{3} and M\'oricz \cite{28}. Here we generalize these theorems to (C; i) statistical limitable method.
View article: ON ABEL CONVERGENT SERIES OF FUNCTIONS
ON ABEL CONVERGENT SERIES OF FUNCTIONS Open
In this paper, we are concerned with Abel uniform convergence and Abel pointwise convergence of series of real functions where a series of functions Σ fn is called Abel uniformly convergent to a function f if for each " > 0 there is a _ >…