In this paper, we propose a refinement in the analytical definition of the s2-convex classes of functions aiming to progress further in the direction of including s2-convexity properly in the body of Real Analysis.
Some new Hermite-Hadamard type's integral equations and inequalities are established. The results in [3] and [6] which refined the upper bound of distance between the middle and left of the typical Hermite-Hadamar...Some new Hermite-Hadamard type's integral equations and inequalities are established. The results in [3] and [6] which refined the upper bound of distance between the middle and left of the typical Hermite-Hadamard's integral inequality are generalized.展开更多
The main purpose of this survey paper is to point out some very recent developments on Simpson’s inequality for strongly extended s-convex function. Firstly, the concept of strongly extended s-convex function is intr...The main purpose of this survey paper is to point out some very recent developments on Simpson’s inequality for strongly extended s-convex function. Firstly, the concept of strongly extended s-convex function is introduced. Next a new identity is also established. Finally, by this identity and H?lder’s inequality, some new Simpson type for the product of strongly extended s-convex function are obtained.展开更多
In this note, we discuss the definition of the S1-convexity Phenomenon. We first make use of some results we have attained for?? in the past, such as those contained in [1], to refine the definition of the phenomenon....In this note, we discuss the definition of the S1-convexity Phenomenon. We first make use of some results we have attained for?? in the past, such as those contained in [1], to refine the definition of the phenomenon. We then observe that easy counter-examples to the claim extends K0 are found. Finally, we make use of one theorem from [2] and a new theorem that appears to be a supplement to that one to infer that? does not properly extend K0 in both its original and its revised version.展开更多
In this note, we analyze a few major claims about . As a consequence, we rewrite a major theorem, nullify its proof and one remark of importance, and offer a valid proof for it. The most important gift of this paper i...In this note, we analyze a few major claims about . As a consequence, we rewrite a major theorem, nullify its proof and one remark of importance, and offer a valid proof for it. The most important gift of this paper is probably the reasoning involved in all: We observe that a constant, namely t, has been changed into a variable, and we then tell why such a move could not have been made, we observe the discrepancy between the claimed domain and the actual domain of a supposed function that is created and we then explain why such a function could not, or should not, have been created, along with others.展开更多
In the paper, the authors find some new inequalities of Hermite-Hadamard type for functions whose third derivatives are s-convex and apply these inequalities to discover inequalities for special means.
文摘In this paper, we propose a refinement in the analytical definition of the s2-convex classes of functions aiming to progress further in the direction of including s2-convexity properly in the body of Real Analysis.
基金Supported by the key scientific and technological innovation team project in shaanxi province(2014KCT-15)the Foundations of Shaanxi Educational committee(NO.18Jk0152)
文摘Some new Hermite-Hadamard type's integral equations and inequalities are established. The results in [3] and [6] which refined the upper bound of distance between the middle and left of the typical Hermite-Hadamard's integral inequality are generalized.
文摘The main purpose of this survey paper is to point out some very recent developments on Simpson’s inequality for strongly extended s-convex function. Firstly, the concept of strongly extended s-convex function is introduced. Next a new identity is also established. Finally, by this identity and H?lder’s inequality, some new Simpson type for the product of strongly extended s-convex function are obtained.
文摘In this note, we discuss the definition of the S1-convexity Phenomenon. We first make use of some results we have attained for?? in the past, such as those contained in [1], to refine the definition of the phenomenon. We then observe that easy counter-examples to the claim extends K0 are found. Finally, we make use of one theorem from [2] and a new theorem that appears to be a supplement to that one to infer that? does not properly extend K0 in both its original and its revised version.
文摘In this note, we analyze a few major claims about . As a consequence, we rewrite a major theorem, nullify its proof and one remark of importance, and offer a valid proof for it. The most important gift of this paper is probably the reasoning involved in all: We observe that a constant, namely t, has been changed into a variable, and we then tell why such a move could not have been made, we observe the discrepancy between the claimed domain and the actual domain of a supposed function that is created and we then explain why such a function could not, or should not, have been created, along with others.
文摘In the paper, the authors find some new inequalities of Hermite-Hadamard type for functions whose third derivatives are s-convex and apply these inequalities to discover inequalities for special means.
