Some properties of strongly convexfunctions are presented. A characterization of pairs of functions that can be separated by a strongly convex function and a Hyers-Ulam stability result for strongly convexfunctions ...
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Some properties of strongly convexfunctions are presented. A characterization of pairs of functions that can be separated by a strongly convex function and a Hyers-Ulam stability result for strongly convexfunctions are given. An integral Jensen-type inequality and a Hermite-Hadamard-type inequality for strongly convexfunctions are obtained. Finally, a relationship between strong convexity and generalizedconvexity in the sense of Beckenbach is shown.
In this paper, we establish double inequalities for twice local fractional differentiable mappings on fractal sets R-alpha(0 < alpha <= 1) of real line numbers. We also give some generalized Hermite-Hadamard lik...
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In this paper, we establish double inequalities for twice local fractional differentiable mappings on fractal sets R-alpha(0 < alpha <= 1) of real line numbers. We also give some generalized Hermite-Hadamard like inequalities for local fractional integrals.
In this paper we deal with functions related to generalizedconvexity and refine Jensen type inequalities satisfied by such functions. Specifically, we extend inequalities satisfied by uniformly convexfunctions, stro...
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In this paper we deal with functions related to generalizedconvexity and refine Jensen type inequalities satisfied by such functions. Specifically, we extend inequalities satisfied by uniformly convexfunctions, strongly convexfunctions as well as superquadratic functions.
In the paper, we extend some previous results dealing with the Hermite-Hadamard inequalities with fractal sets and several auxiliary results that vary with local fractional derivatives introduced in the recent literat...
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In the paper, we extend some previous results dealing with the Hermite-Hadamard inequalities with fractal sets and several auxiliary results that vary with local fractional derivatives introduced in the recent literature. We provide new generalizations for the third-order differentiability by employing the local fractional technique for functions whose local fractional derivatives in the absolute values are generalizedconvex and obtain several bounds and new results applicable to convexfunctions by using the generalized Holder and power-mean *** an application, numerous novel cases can be obtained from our outcomes. To ensure the feasibility of the proposed method, we present two examples to verify the method. It should be pointed out that the investigation of our findings in fractal analysis and inequality theory is vital to our perception of the real world since they are more realistic models of natural and man-made phenomena.
A class of multi-objective fractional programming problems (MFP) are considered where the involved functions are locally Lipschitz. In order to deduce our main results, we give the definition of the generalized (F,the...
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A class of multi-objective fractional programming problems (MFP) are considered where the involved functions are locally Lipschitz. In order to deduce our main results, we give the definition of the generalized (F,theta,rho,d)-convex class about the Clarke's generalized gradient. Under the above generalizedconvexity assumption, necessary and sufficient conditions for optimality are given. Finally, a dual problem corresponding to (MFP) is formulated, appropriate dual theorems are proved.
A class of multi-objective fractional programming problems (MFP) are considered where the involved functions are locally Lipschitz. In order to deduce our main results, we give the definition of the generalized (F,the...
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A class of multi-objective fractional programming problems (MFP) are considered where the involved functions are locally Lipschitz. In order to deduce our main results, we give the definition of the generalized (F,theta,rho,d)-convex class about the Clarke's generalized gradient. Under the above generalizedconvexity assumption, necessary and sufficient conditions for optimality are given. Finally, a dual problem corresponding to (MFP) is formulated, appropriate dual theorems are proved.
The notion of s-monotone polarity for s-subdifferential is introduced and studied. Also, the concept of Frechet s-subdifferential is introduced and then some results regarding this concept are obtained. In addition, s...
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The notion of s-monotone polarity for s-subdifferential is introduced and studied. Also, the concept of Frechet s-subdifferential is introduced and then some results regarding this concept are obtained. In addition, some particular relationships between the s-subdifferential and Frechet s-subdifferential are presented.
In the present paper, we first establish a general parameterized identity for local fractional twice differentiable functions involving extended fractal-fractional integral operators. Thus by employing generalized con...
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In the present paper, we first establish a general parameterized identity for local fractional twice differentiable functions involving extended fractal-fractional integral operators. Thus by employing generalizedconvexity on differentiable mappings along with Yang's Power-mean, Holder's and improved fractal integral inequalities lead us to develop variety of new fractal-fractional parameterized inequalities. Several examples are provided with graphical illustrations to prove the validity of new results. We give error analysis of improved bounds numerically and also by 2D, 3D graphical representations. Finally, we show that our main results recapture fractal variants of trapezoid, midpoint, Simpson and Bullen-type inequalities. Some related applications to the fractal means, moment of random variables and wave equations are given as well.
In the present work we show that the local generalized monotonicity of a lower semicontinuous set-valued operator on some certain type of dense sets ensures the global generalized monotonicity of that operator. We ach...
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In the present work we show that the local generalized monotonicity of a lower semicontinuous set-valued operator on some certain type of dense sets ensures the global generalized monotonicity of that operator. We achieve this goal gradually by showing at first that the lower semicontinuous set-valued functions of one real variable, which are locally generalized monotone on a dense subsets of their domain are globally generalized monotone. Then, these results are extended to the case of set-valued operators on arbitrary Banach spaces. We close this work with a section on the global generalizedconvexity of a real valued function, which is obtained out of its local counterpart on some dense sets.
generalizedconvex vector functions are characterized by using order preserving transformations and some calculus rules for subdifferential of convex vector functions are obtained.
generalizedconvex vector functions are characterized by using order preserving transformations and some calculus rules for subdifferential of convex vector functions are obtained.
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