Type Integral Inequalities Research Articles

Fractional trapezium type inequalities for twice differentiable preinvex functions and their applications

Trapezoidal inequalities for functions of divers natures are useful in numerical computations. The authors have proved an identity for a generalized integral operator via twice differentiable preinvex function. By applying the established identity, the generalized trapezoidal type integral inequalities have been discovered. It is pointed out that the results of this research provide integral inequalities for almost all fractional integrals discovered in recent past decades. Various special cases have been identified. Some applications of presented results to special means have been analyzed. The ideas and techniques of this paper may stimulate further research.

On Impulsive Delay Integrodifferential Equations with Integral Impulses

The present research paper is devoted to investigate the existence, uniqueness of mild solutions for impulsive delay integrodifferential equations with integral impulses in Banach spaces. We also investigate the dependence of solutions on initial conditions, parameters and the functions involved in the equations. Our analysis is based on semigroup theory, fixed point technique and an application of Pachpatte's type integral inequality with integral impulses. An example is provided in support of existence result.

Some Hermite–Hadamard type integral inequalities for convex functions defined on convex bodies in ℝn\mathbb{R}^{n}

Abstract In this paper, by the use of the divergence theorem, we establish some integral inequalities of Hermite–Hadamard type for convex functions of several variables defined on closed and bounded convex bodies in the Euclidean space ℝ n {\mathbb{R}^{n}} for any n ≥ 2 {n\geq 2} .

Generalized trapezoidal type integral inequalities and their applications

The authors have proved an identity for a generalized integral operator via differentiable function. By applying the established identity and using the new and improved form of Holder’s integral inequality called Holder–Iscan integral inequality, some new generalized trapezoidal type integral inequalities have been obtain. Various special cases have been identified. Some applications to special means and error estimations of presented results have been analyzed.

Exponential type convexity and some related inequalities

In this manuscript, we give and study the concept of exponential type convex functions and some of their algebraic properties. We prove two Hermite–Hadamard (H-H) type integral inequalities for the newly introduced class of functions. We also obtain some refinements of the H-H inequality for functions whose first derivative in absolute value at certain power is exponential type convex.

Fixed-Point Theorems for α-Admissible Mappings with w-Distance and Applications to Nonlinear Integral Equations

Two fixed-point theorems for α-admissible mappings satisfying contractive inequality of integral type with w-distance in complete metric spaces are proved. Our results extend and improve a few existing results in the literature. As applications, we use the fixed-point theorems obtained in this paper to establish solvability of nonlinear integral equations. Examples are included.

Generalized fractional maximal operator on generalized local Morrey spaces

In this paper, we study the boundedness of generalized fractional maximal operator on generalized local Morrey spaces and generalized Morrey spaces, including weak estimates. Firstly, we prove the Spanne type boundedness of generalized fractional maximal operator on generalized local Morrey spaces for 1 < p < q < infinity and, on weak generalized local Morrey spaces for p = 1 and 1 < q < infinity . Secondly, we prove the Adams type boundedness of generalized fractional maximal operator on generalized local Morrey spaces for 1 < p < q < \infinity and, on weak generalized local Morrey spaces for p = 1 and 1 < q < infinity . In all cases the conditions for the boundedness of generalized fractional maximal operators are given in terms of supremal- type integral inequalities on (\varphi_1; \varphi_ 2; \rho) and ( \varphi ; \rho), which do not assume any assumption on monotonicity of \varphi_ 1(x; r), \varphi_ 2(x; r) and \varphi (x; r) in r.

Delay dynamic double integral inequalities on time scales with applications

In the article, we present the explicit bounds for three generalized delay dynamic Gronwall–Bellman type integral inequalities on time scales, which are the unification of continuous and discrete results. As applications, the boundedness for the solutions of delay dynamic integro-differential equations with initial conditions is discussed.

Some Hermite–Hadamard type integral inequalities for multidimensional general preinvex stochastic processes

In this study, we initially defined general preinvexity for real valued stochastic processes. Correspondingly, we also established multidimensional general preinvex stochastic processes which are a significant class of stochastic processes for optimization. Moreover, we obtained Hermite–Hadamard type integral inequalities for before mentioned processes using mean-square integrability.

General Convexity of Multidimensional Functions and Related Hermite-Hadamard Type Integral Inequalities

The basic goal is to investigate general convexity of multidimensional functions and derive several important inequalities associated with it’s in this paper. For this reason, multidimensional general convex functions were firstly defined. Afterwards, some properties of these functions were mentioned. Accordingly, the relation of multidimensional general convex functions with other convex functions was established. Additionally, a generalization of Hermite-Hadamard type integral inequality was showed for two-dimensional general convex functions. Finally , Hermite-Hadamard type integral inequality for multidimensional general convex functions was verified and an explanatory example for this inequality was given in this study.

Simpson’s type inequalities for η-convex functions via k-Riemann–Liouville fractional integrals

We introduce some Simpson's type integral inequalities via k-Riemann–Liouville fractional integrals for functions whose derivatives are η-convex. These results generalize some results in the literature.

Some estimates on the weighted Simpson-like type integral inequalities and their applications

Some estimates on the weighted Simpson-like type integral inequalities and their applications

Some new integral inequalities via Steklov operator

Hardy and Copson type inequalities have been studied by a large number of authors during the twentieth century and has motivated some important lines of study which are currently active. A large number of papers have been appeared involving Copson and Hardy inequalities (see [2-16] for more details). In this paper some Hardy-Steklov and Copson-Steklov type integral inequalities were established.

On some fractional integral inequalities for generalized strongly modified $h$-convex functions

Convex functions play an important role in many areas of mathematics. They are especially important in the study of optimization problems where they are distinguished by a number of convenient properties. Many generalizations of convex functions exists in literature. The main aim of the article is to develop fractional integral inequalities for generalized strongly modified h-convex functions. Based on obtained fractional type integral inequalities we give some applications to the means. Our results are extension and generalization of many existing results.

Some New $(p_1p_2,q_1q_2)$-Estimates of Ostrowski-type integral inequalities via &lt;i&gt;n&lt;/i&gt;-polynomials &lt;i&gt;s&lt;/i&gt;-type convexity

The purpose of this paper is to establish new generalization of Ostrowski type integral inequalities by using $(p, q)$-analogues which are related to the estimates of upper bound for a class of $(p_1p_2, q_1q_2)$-differentiable functions on co-ordinates. We first establish an integral identity for $(p_1p_2, q_1q_2)$-differentiable functions on co-ordinates. The result is then used to derive some estimates of upper bound for the functions whose twice partial $(p_1p_2, q_1q_2)$-differentiable functions are $n$-polynomial $s$-type convex functions on co-ordinates. Some new special cases from the main results are obtained and some known results are recaptured as well. At the end, an application to special means is given as well.

Chebyshev type inequalities involving extended generalized fractional integral operators

In this paper, mainly by using the extended generalized fractional integral operator that involve a further extension of Mittag-Leffler function in the kernel, we obtain several fractional Chebyshev type integral inequalities. So, results of Dahmani et al. from [ 4 ] are generalized. Also, it is point out that new results are obtained for different fractional integral operators with the help of special selection of parameters.

Fixed point theorems for quadruple self-mappings satisfying integral type inequalities

In this paper, we study the generalization of (S,F)-rational contraction pair (h; 1) to almost (S,F,?)-rational contraction pair (h,g) of integral type on metric spaces. Further, we use the new generalized notion to produce some fixed point theorems via integral inequalities. This work generalizes many results in the available literature. For demonstration we give examples which show that our work generalizes many results.

HALF-LINEAR VOLTERRA-FREDHOLM TYPE INTEGRAL INEQUALITIES ON TIME SCALES AND THEIR APPLICATIONS

The main aim of this paper is to establish some new half-linear Volterra-Fredholm type integral inequalities on time scales. Our results not only extend and complement some known integral inequalities but also provide an effective tool for the study of qualitative properties of solutions of some dynamic equations.

Log m-Convex Functions

Abstract In this research we lay the concept of log m-convex functions defined on real intervals containing the origin, some algebraic properties are exhibit, in the same token discrete Jensen type inequalities and integral inequalities are set and shown.

Fractional Hermite-Hadamard type integral inequalities for functions whose modulus of the mixed derivatives are co-ordinated s-preinvex in the second sense

Abstract In this paper we establish some fractional Hermite-Hadamard type integral inequalities for functions whose modulus of the mixed derivatives are co-ordinated s-preinvex in the second sense.