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.
In this paper a general theorem on the replacement of the condition “for all λ in the definition of generalizedconvexity properties of lower semicontinuous functions by the condition “there exists a λ” is shown....
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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,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 nonlinear multiple objective programming problem is considered where the functions involved are nondifferentiable. By considering the concept of weak minima, the Fritz John type and Karush-Kuhn-Tucker type necessary...
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A nonlinear multiple objective programming problem is considered where the functions involved are nondifferentiable. By considering the concept of weak minima, the Fritz John type and Karush-Kuhn-Tucker type necessary optimality conditions and Wolfe and Mond-Weir type duality results are given in terms of the right differentials of the functions. The duality results are stated by using the concepts of generalized semilocally convexfunctions.
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.
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.
In this article, we establish a new auxiliary identity on fractal sets for twice local differentiable function involving extended fractal integral operators. Testing this identity together with generalized fractal Hol...
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In this article, we establish a new auxiliary identity on fractal sets for twice local differentiable function involving extended fractal integral operators. Testing this identity together with generalized fractal Holder's and Power-mean integral inequalities, we develop some new fractal-fractional Simpson's type inequalities. Furthermore, we use modified Yang Holder's and Power-mean inequality to create new fractal estimates. We also give comparison analysis of bounds and show how the modified form of Yang Holder's and Power-mean integral inequalities can result in improved lower upper bounds. We also provide concrete examples to examine the validity of obtain results numerically and also justify them by 2D and 3D graphical analysis. As implementations, we operate our findings to get new applications in form of..-type special means, moment of random variables and wave equations.
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