In this paper, we establish a new refinement of Jensen-type inequality for uniformly convex funct... more In this paper, we establish a new refinement of Jensen-type inequality for uniformly convex functios. Furthermore, we apply those results in information theory and we obtain strong and more precise bounds for Shannon's entropy.
Convex sets and convex functions play a fundamental role in the development of various fields of ... more Convex sets and convex functions play a fundamental role in the development of various fields of pure and applied mathematics. Recently, many new generalizations of inequalities with respect to Hermite-Hadamard have been proposed in the literature. In this paper, some new inequalities of the Hermite-Hadamard type for differentiable convex functions are given. These new inequalities are based on the second derivative functions.
In this paper, we first define a new pseudo-metric d on a normed linear space X. We do this by in... more In this paper, we first define a new pseudo-metric d on a normed linear space X. We do this by introducing two different classes of elementary topical functions. Next, we use this pseudo-metric d to investigate the non-expansivity and some properties of topical functions. Finally, the characterizations of fixed points of topical functions are given, and a relation between the pseudo-metric d and the original norm of the normed linear space X is presented.
Numerical Functional Analysis and Optimization, Jun 17, 2016
ABSTRACT In this article, we study topical functions f:X→K defined on a b-complete idempotent sem... more ABSTRACT In this article, we study topical functions f:X→K defined on a b-complete idempotent semimodule X over a b-complete idempotent semifield K with values in K. We characterize the abstract concavity and support set of this class of functions. Next, we investigate the abstract concavity of extended valued topical functions , where and ⊤: = supK. Finally, as an application, we present characterizations of upward and downward sets by using extended valued elementary topical functions.
In this paper, we prove Hermite-Hadamard inequality for uniformly convex, uniformly s-convex func... more In this paper, we prove Hermite-Hadamard inequality for uniformly convex, uniformly s-convex functions. Also, we obtain Hermite Hadamard inequality for fractional integral by using these functions. Finally, some applications of these inequalities are given.
In this paper, we have established some new integral identities connected with the left-hand side... more In this paper, we have established some new integral identities connected with the left-hand side of Hermite–Hadamard inequality. By using this identity, we have obtained some new bounds for functions whose derivatives in absolute values are s-convex.
The normalised Jensen functional is an important functional in theory of inequalities and it has ... more The normalised Jensen functional is an important functional in theory of inequalities and it has been a subject of study in its own right. In this paper, we establish new bounds for Jensen’s discrete inequality. Also, we improve the basic result of Dragomir through a stronger refinement of Jensens inequality which is then applied to analysis and information theory.
In this paper, we establish Hermite-Hadamard inequalities for uniformly p-convex functions and un... more In this paper, we establish Hermite-Hadamard inequalities for uniformly p-convex functions and uniformly q-convex functions. Also, we obtain some new inequalities of Hermite-Hadamard type for functions whose derivatives in absolute value are the class of uniformly p-convex.
Convex sets and convex functions play a fundamental role in the development of various fields of ... more Convex sets and convex functions play a fundamental role in the development of various fields of pure and applied mathematics. Recently, many new generalizations of inequalities with respect to Hermite-Hadamard have been proposed in the literature. In this paper, some new inequalities of the Hermite-Hadamard type for differentiable convex functions are given. These new inequalities are based on the second derivative functions.
In this paper, we study abstract convexity topical and sub-topical functions. We obtain some resu... more In this paper, we study abstract convexity topical and sub-topical functions. We obtain some results on abstract convexity such as support set and subdifferential in view of new elementary functions. Indeed, first we show that the ICR and IR functions are dense in IPH functions then the topical function and sub-topical function on topological vector space by another elementary function is studied. These elementary functions lead to obtain similar results with easier proofs.
In this paper, we have established some new integral identities connected with the left-hand side... more In this paper, we have established some new integral identities connected with the left-hand side of Hermite–Hadamard inequality. By using this identity, we have obtained some new bounds for functions whose derivatives in absolute values are s-convex.
In this paper, we establish a new refinement of Jensen-type inequality for uniformly convex funct... more In this paper, we establish a new refinement of Jensen-type inequality for uniformly convex functios. Furthermore, we apply those results in information theory and we obtain strong and more precise bounds for Shannon's entropy.
Convex sets and convex functions play a fundamental role in the development of various fields of ... more Convex sets and convex functions play a fundamental role in the development of various fields of pure and applied mathematics. Recently, many new generalizations of inequalities with respect to Hermite-Hadamard have been proposed in the literature. In this paper, some new inequalities of the Hermite-Hadamard type for differentiable convex functions are given. These new inequalities are based on the second derivative functions.
In this paper, we first define a new pseudo-metric d on a normed linear space X. We do this by in... more In this paper, we first define a new pseudo-metric d on a normed linear space X. We do this by introducing two different classes of elementary topical functions. Next, we use this pseudo-metric d to investigate the non-expansivity and some properties of topical functions. Finally, the characterizations of fixed points of topical functions are given, and a relation between the pseudo-metric d and the original norm of the normed linear space X is presented.
Numerical Functional Analysis and Optimization, Jun 17, 2016
ABSTRACT In this article, we study topical functions f:X→K defined on a b-complete idempotent sem... more ABSTRACT In this article, we study topical functions f:X→K defined on a b-complete idempotent semimodule X over a b-complete idempotent semifield K with values in K. We characterize the abstract concavity and support set of this class of functions. Next, we investigate the abstract concavity of extended valued topical functions , where and ⊤: = supK. Finally, as an application, we present characterizations of upward and downward sets by using extended valued elementary topical functions.
In this paper, we prove Hermite-Hadamard inequality for uniformly convex, uniformly s-convex func... more In this paper, we prove Hermite-Hadamard inequality for uniformly convex, uniformly s-convex functions. Also, we obtain Hermite Hadamard inequality for fractional integral by using these functions. Finally, some applications of these inequalities are given.
In this paper, we have established some new integral identities connected with the left-hand side... more In this paper, we have established some new integral identities connected with the left-hand side of Hermite–Hadamard inequality. By using this identity, we have obtained some new bounds for functions whose derivatives in absolute values are s-convex.
The normalised Jensen functional is an important functional in theory of inequalities and it has ... more The normalised Jensen functional is an important functional in theory of inequalities and it has been a subject of study in its own right. In this paper, we establish new bounds for Jensen’s discrete inequality. Also, we improve the basic result of Dragomir through a stronger refinement of Jensens inequality which is then applied to analysis and information theory.
In this paper, we establish Hermite-Hadamard inequalities for uniformly p-convex functions and un... more In this paper, we establish Hermite-Hadamard inequalities for uniformly p-convex functions and uniformly q-convex functions. Also, we obtain some new inequalities of Hermite-Hadamard type for functions whose derivatives in absolute value are the class of uniformly p-convex.
Convex sets and convex functions play a fundamental role in the development of various fields of ... more Convex sets and convex functions play a fundamental role in the development of various fields of pure and applied mathematics. Recently, many new generalizations of inequalities with respect to Hermite-Hadamard have been proposed in the literature. In this paper, some new inequalities of the Hermite-Hadamard type for differentiable convex functions are given. These new inequalities are based on the second derivative functions.
In this paper, we study abstract convexity topical and sub-topical functions. We obtain some resu... more In this paper, we study abstract convexity topical and sub-topical functions. We obtain some results on abstract convexity such as support set and subdifferential in view of new elementary functions. Indeed, first we show that the ICR and IR functions are dense in IPH functions then the topical function and sub-topical function on topological vector space by another elementary function is studied. These elementary functions lead to obtain similar results with easier proofs.
In this paper, we have established some new integral identities connected with the left-hand side... more In this paper, we have established some new integral identities connected with the left-hand side of Hermite–Hadamard inequality. By using this identity, we have obtained some new bounds for functions whose derivatives in absolute values are s-convex.
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Papers by hasan barsam