Hermite‐Hadamard‐type inequalities for interval‐valued coordinated convex functions involving generalized fractional integrals
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DOI: 10.1002/mma.6712
Abstract: In this paper, we define interval‐valued left‐sided and right‐sided generalized fractional double integrals. We establish inequalities of Hermite‐Hadamard like for coordinated interval‐valued convex functions by applying our newly defined integrals. read more here.
Keywords: generalized fractional; hermite hadamard; type inequalities; hadamard type ... See more keywords
Unified Approach to Starlike and Convex Functions Involving Convolution Between Analytic Functions
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DOI: 10.1007/s00025-018-0782-0
Abstract: Using the idea of convolution between analytic functions, we define a class $$\mathcal {UM}(g,\gamma ,b,k)$$UM(g,γ,b,k) of analytic functions comprising of starlike and convex functions. These functions map the open unit disc on to the conic… read more here.
Keywords: convolution analytic; starlike convex; analytic functions; convex functions ... See more keywords
On the Raşa Inequality for Higher Order Convex Functions
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DOI: 10.1007/s00025-021-01417-2
Abstract: We study the following $$(q-1)$$ th convex ordering relation for qth convolution power of the difference of probability distributions $$\mu $$ and $$\nu $$ $$\begin{aligned} (\nu -\mu )^{*q}\ge _{(q-1)cx} 0 , \quad q\ge 2, \end{aligned}$$… read more here.
Keywords: order convex; inequality; higher order; convex functions ... See more keywords
Trapezoidal (p,q)-Integral Inequalities Related to (η1,η2)-convex Functions with Applications
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DOI: 10.1007/s10773-021-04739-7
Abstract: In this paper, the authors introduce the (p,q)-trapezoidal integral inequalities, which are the (p,q)-analogues of the recently introduced q-trapezoidal integral inequalities. We derive a new (p,q)-integral identity for twice (p,q)-differentiable function. Utilizing this as an… read more here.
Keywords: inequalities related; related convex; integral inequalities; convex functions ... See more keywords
On the Strong Convergence of Subgradients of Convex Functions
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DOI: 10.1007/s10957-018-1276-7
Abstract: In this paper, results on the strong convergence of subgradients of convex functions along a given direction are presented; that is, the relative compactness (with respect to the norm) of the union of subdifferentials of… read more here.
Keywords: convergence subgradients; subgradients convex; strong convergence; convex functions ... See more keywords
A Note on the Optimal Convergence Rate of Descent Methods with Fixed Step Sizes for Smooth Strongly Convex Functions
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DOI: 10.1007/s10957-022-02032-z
Abstract: Based on a result by Taylor et al. (J Optim Theory Appl 178(2):455–476, 2018) on the attainable convergence rate of gradient descent for smooth and strongly convex functions in terms of function values, an elementary… read more here.
Keywords: convergence; descent; convergence rate; convex functions ... See more keywords
New Fractional Integral Inequalities for Differentiable Convex Functions and Their Applications
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DOI: 10.1007/s11253-017-1376-9
Abstract: We establish some new fractional integral inequalities for differentiable convex functions and give several applications for the Beta-function. read more here.
Keywords: new fractional; convex functions; integral inequalities; inequalities differentiable ... See more keywords
On generalized convex functions and generalized subdifferential II
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DOI: 10.1007/s11590-020-01682-0
Abstract: We introduce and study the notion of the $$\left( \sigma ,y\right) $$ σ , y -conjugate of a proper $$\sigma $$ σ -convex function. Some relations between the $$\sigma $$ σ -subdifferentials and the Clarke–Rockafellar… read more here.
Keywords: convex functions; generalized convex; functions generalized; sigma ... See more keywords
The DTC (difference of tangentially convex functions) programming: optimality conditions
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DOI: 10.1007/s11750-021-00615-z
Abstract: We focus on optimality conditions for an important class of nonconvex and nonsmooth optimization problems, where the objective and constraint functions are presented as a difference of two tangentially convex functions. The main contribution of… read more here.
Keywords: optimality conditions; optimality; convex functions; tangentially convex ... See more keywords
Zeros of holomorphic functions in the unit disk and $$\rho $$ρ-trigonometrically convex functions
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DOI: 10.1007/s13324-019-00282-1
Abstract: Let M be a subharmonic function with Riesz measure $$\mu _M$$μM on the unit disk $${\mathbb {D}}$$D in the complex plane $${\mathbb {C}}$$C. Let f be a nonzero holomorphic function on $${\mathbb {D}}$$D such that… read more here.
Keywords: trigonometrically convex; rho trigonometrically; unit disk; convex functions ... See more keywords
Weighted averages of n-convex functions via extension of Montgomery’s identity
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DOI: 10.1007/s40065-019-0245-9
Abstract: Using an extension of Montgomery’s identity and the Green’s function, we obtain new identities and related inequalities for weighted averages of n-convex functions, i.e. the sum $$\sum _{i=1}^m \rho _i h(\lambda _i)$$∑i=1mρih(λi) and the integral… read more here.
Keywords: montgomery identity; weighted averages; averages convex; convex functions ... See more keywords